Cost Evaluation of a Two-Echelon Inventory System with Lost Sales and Approximately Normal

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Efficiency and risk in Japanese banking

E ciency and risk in Japanese bankingYener Altunbas a ,Ming-Hau Liu b ,Philip Molyneuxc,*,Rama Seth d,1aThe Business School,South Bank University,Southwark Campus,103Borough Road,London,SE10AA,UKbNanyang Business School,NTU,Singapore 639798,SingaporecSchool of Accounting,Banking and Economics,University of Wales Bangor,Gwynedd,Bangor,LL572DG,UKdFederal Reserve Bank of New York,New York,NY 10045,USAReceived 18April 1997;accepted 27July 1999AbstractThis paper investigates the impact of risk and quality factors on banks Õcost by using the stochastic cost frontier methodology to evaluate scale and X -ine ciencies,as well as technical change for a sample of Japanese commercial banks between 1993and 1996.Loan-loss provisions are included in the cost frontier model to control for output quality,with a ®nancial capital and a liquidity ratio included to control risk.Following the ap-proach suggested in Mester (1996)we show that if risk and quality factors are not taken into account optimal bank size tends to be overstated.That is,optimal bank size is considerably smaller when risk and quality factors are taken into account when mod-elling the cost characteristics of Japanese banks.We also ®nd that the level of ®nancial capital has the biggest in¯uence on the scale e ciency estimates.X -ine ciency estimates,in contrast,appear less sensitive to risk and quality factors.Our results also suggest that scale ine ciencies dominate X -ine ciencies.These are important ®ndings because they contrast with the results of previous studies on Japanese banking.In particular,the results indicate an alternative policy prescription,namely,that the largest banks shouldJournal of Banking &Finance 24(2000)1605±1628/locate/econbase*Corresponding author.Tel.:+44-1248-382170;fax:+44-1248-364760.E-mail address:p.molyneux@ (P.Molyneux).1The views expressed are those of the author and do not necessarily re¯ect those of the Federal Reserve Bank of New York or the Federal Reserve System.0378-4266/00/$-see front matter Ó2000Elsevier Science B.V.All rights reserved.PII:S 0378-4266(99)00095-31606Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628shrink to bene®t from scale advantages.It also seems that®nancial capital has the largest in¯uence on optimal bank size.Ó2000Elsevier Science B.V.All rights reserved.JEL classi®cation:G21;D21;G23Keywords:Japanese banks;Cost functions;Economies of scale;Ine ciencies;Technical change1.IntroductionStudies of the Japanese banking industry have typically found strong evi-dence of scale economies across a broad range of bank sizes(see for example, Kasuya,1986;Yoshioka and Nakajima,1987;Tachibanaki et al.,1991; Fukuyama,1993;McKillop et al.,1996).The aforementioned studies provide an indication of the cost characteristics of the Japanese banking industry, however,they may be limited because they do not take into account the risks associated with banks'operations.This is a particularly relevant issue in Japanese banking given that the system has experienced substantial asset quality problems and low levels of capitalisation since the early1990s(see Bank of Japan,1995,1996).Recent studies such as those Hughes and Mester (1993),Hughes et al.(1995),McAllister and McManus(1993),Mester(1996) and Clark(1996)have drawn attention to the fact that bank e ciency studies typically ignore the impact of risk on banks'costs or pro®ts and they suggest that risk characteristics need to be incorporated in the underlying industry cost or pro®t functions because,`unless quality and risk are controlled for,one might easily miscalculate a bank's level of ine ciency'(Mester,1996,p.1026). For instance,Hughes et al.(1995)in their study on1989±90US banks which exceed$1billion in asset size,®nd that when they control for risk,inexhaustible economies of scale that increase with size are prevalent.When risk neutrality is imposed on the estimation,the large scale economies disappear and constant returns to scale are obtained.McAllister and McManus(1993)also show that for larger US banks estimates of scale economies are increased when they control for risk.(This tends to be more prevalent for banks up to$1billion in asset size.)In contrast,Hughes and Mester(1993)®nd that estimates of in-creasing returns to scale for a wide range of bank sizes become constant returns when asset quality,®nancial capital and risk are taken into account.Clark (1996)also re-emphasises the in¯uence of risk factors in the cost characteristics of US banks and shows how risk can statistically in¯uence e ciency levels±in particular,he shows how X-ine ciency estimates tend to become smaller (about3%from9%)when risk factors are incorporated in frontier estimations. In order to advance the aforementioned literature,this paper evaluates cost e ciency and technical change for Japanese commercial banks by comparingY.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281607 results obtained from two cost functions speci®cations.First we use the sto-chastic cost frontier methodology to estimate scale economies,scale e ciencies and X-ine ciency,as well as technical change,for a sample of Japanese commercial banks between1993and1996using a three input±three output Fourier-¯exible cost function speci®cation.The three outputs include total loans,total securities and total o -balance sheet items(nominal value).We then compare these results with those generated by a similar cost function which also includes variables controlling for risk and quality factors.In ad-dition,we also evaluate the sensitivity of scale economy and X-ine ciency estimates to various risk and quality variables.Our results show that when the underlying cost function speci®cation does not control for risk and quality factors,scale economies are prevalent for all but the largest Japanese banks.Those larger than Yen10,000billion exhibit signi®cant diseconomies.Overall,Japanese banks appear to be relatively scale e cient.When risk and quality factors are taken into account,however,only the very smallest banks exhibit signi®cant economies with the majority of banks experiencing signi®cant diseconomies of scale which appear to get larger with asset size.Estimates derived from the model including risk and quality variables suggested that there are widespread scale ine ciencies in the Japanese banking market.These results suggest that bank minimum e cient scale be-comes smaller after controlling for risk,a®nding similar to that of Hughes and Mester(1993).This contrasts with the results of Hughes et al.(1995)and McAllister and McManus(1993)who®nd either minimum e cient scale is increased or scale economies are never exhausted after controlling for risk.Our results also point to the limitations of previous studies on the cost character-istics of Japanese banking and also suggest di erent policy conclusions, namely,that the largest banks should reduce their size if they wish to bene®t from scale economies.In contrast to the scale estimates and ClarkÕs(1996)®ndings on US banking,X-ine ciency scores appear to be less sensitive to the inclusion of risk and quality variables.The mean level of X-ine ciency for the largest banks range between5%and7%.This also indicates that the largest Japanese banks should focus on reducing managerial and other ine ciencies, as well as reducing their size if they are to generate cost savings.Finally,this study also®nds that technical change has reduced bank cost,but at a declining rate,between1993and1996.2.MethodologyFollowing Mester(1996),Cebenoyan et al.(1993)and Allen and Rai(1996) we use the stochastic cost frontier methodology.This approach labels a bank as ine cient if its costs are higher than those predicted for an e cient bank producing the same input/output con®guration and the di erence cannot beexplained by statistical noise.The cost frontier is obtained by estimating a Fourier Flexible cost function with a composite error term,the sum of a two-sided error representing random¯uctuations in cost and a one-sided positive error term representing ine ciency.The single-equation stochastic cost function model can be given asTC TC Q i Y P i e i Y 1 where TC is observed total cost,Q i is a vector of outputs,and P i is an input price vector.Following Aigner et al.(1977),we assume that the error term of the cost function ise u v Y 2 where u and v are independently distributed.u is usually assumed to be dis-tributed as half-normal,that is,a one-sided positive disturbance capturing the e ects of ine ciency,and v is assumed to be distributed as two-sided normal with zero mean and variance r2,capturing the e ects of the statistical noise. Observation-speci®c estimates of technical ine ciency,u,can be calculated by using the distribution of the ine ciency term conditional on the estimate of the composed error term,as proposed by Jondrow et al.(1982).The mean of this conditional distribution for the half-normal model is shown asE u i j e irk1 k2f e i k a r1ÀF e i k a re i kr!Y 3where F(á)and f(á)are the standard normal distribution and the standard normal density function,respectively.E(u j e)is an unbiased but inconsistent estimator of u i,since regardless of N,the variance of the estimator remains non-zero(see Greene,1993a,pp.80±82).Jondrow et al.(1982)have shown that the ratio of the variability(standard deviation,r)for u and v can be used to measure a bankÕs relative ine ciency,where k r u a r v,is a measure of the amount of variation stemming from ine ciency relative to noise for the sam-ple.Estimates of this model can be computed by maximising the likelihood function directly(see Olson et al.,1980).Kaparakis et al.(1994),Allen and Rai (1996)and Mester(1996)all use the half-normal speci®cation to test for in-e ciency di erences between®nancial institutions mainly in the US market.22See Bauer(1990)for an excellent review of the frontier literature and how di erent stochastic assumptions can be made.Cebenoyan et al.(1993)and Berger and DeYoung(1997),for example, use the truncated normal model.Mester(1993)in common with many(non-banking)studies uses the half-normal distribution.Stevenson(1980)and Greene(1990)have used normal-gamma model. Altunbas and Molyneux(1994)®nd that e ciency estimates are relatively insensitive to di erent distributional assumptions when testing the half normal,truncated normal,normal-exponential and gamma e ciency distributions,as all distributions yield similar ine ciency levels for the German banking markets.1608Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628The Fourier-¯exible cost function used to calculate X-ine ciencies(as well as scale economies and technical change)incorporates a two-component error structure and is estimated using the maximum likelihood procedure.3First we estimate a cost function that controls for risk and quality factors and then we compare the results with those derived from the same cost function excluding all and then individual risk and quality variables(because we use three risk and quality variables there are®ve cost functions estimates in total).The cost function is given aslnTC a03i 1a i ln Q i3i 1b i ln P i s1ln E k1lnNPL a Lk2lnL a TA t1T 123i 13j 1d ij ln Q i ln Q j 43i 1 3j 1c ij ln P i ln P j /1ln E ln E t11T253i 1 3i 1q ij ln P i ln Q j3i 1w i s ln P i ln E3i 1h i s ln Q j ln E3i 1 a i cos z i b i sin z i3i 13j 1a ij cos z i z jb ij sin z i z j e Y 4 where ln TC the natural logarithm of total costs(operating and®nancial cost); ln Q i the natural logarithm of i th bank outputs;ln P i the natural logarithm of i th input prices;ln E the natural logarithm of®nancial capital;4ln NPL/L the3Spong et al.(1995),Berger et al.(1997)and Mitchell and Onvural(1996)have suggested that the Fourier-¯exible functional form should be preferred over the translog because the former better approximates the underlying cost function across a broad range of outputs.The semi-non-parametric Fourier functional form has desirable mathematical and statistical properties because an(in®nite)Fourier series is capable of representing any function exactly and even truncated Fourier series can approximate a function reasonably well throughout its entire range.In contrast, when using parametric methods like the translog,one holds the maintained hypothesis that the bank industryÕs true cost function has the translog form.If this maintained hypothesis is false misspeci®cation error occurs.When using the Fourier functional form,one avoids holding any maintained hypothesis by allowing the data to reveal the true cost function through a large value of ®tted parameters.For ease of exposition,however,we choose to use the translog functional form to illustrate the impact risk and quality factors have on Japanese commercial banksÕcost e ciencies. 4Note that the®nancial capital variable(E)is fully interactive with the output(Q)and input price(P)variables but NPL/L and L/TA are not.This is because the inclusion of more than one of the risk/quality variables would signi®cantly reduce the degrees of freedom,due to the expansion of Fourier terms and the limited number of observations.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281609natural logarithm of the ratio of non-performing loans to total loans;ln L/TA the natural logarithm of the ratio liquid assets to total assets;T time trend; Z i the adjusted values of the log output ln Q i such that they span the interval [0,2p];a,b,d,c,k,/,h,w,q,k,a,b and t are coe cients to be estimated. Since the duality theorem requires that the cost function must be linearly homogeneous in input prices,the following restrictions have to be imposed on the parameters in Eq.(4):3 i 1b i 1Y3i 1c ij 0for all j Y3 i 1q ij 0Y3i 1W ij 0for all j X5Furthermore,the second order parameters of the cost function in Eq.(4)must be symmetric,that is,d ij d ji for all i Y j Yc ij c ji for all i Y j X6For the de®nition of inputs and outputs we use a variation of the intermedi-ation approach proposed by Sealey and Lindley(1977)where the inputs,la-bour,physical capital and deposits are used to produce earning assets.Two of our outputs,total loans and total securities are earning assets and we also include total o -balance sheet items(measured in nominal terms)as a third output.Although the latter are technically not earning assets,this type of business constitutes an increasing source of income for banks and therefore should be included when modelling banks'cost characteristics,otherwise,total output would tend to be understated(Jagtiani and Khanthavit,1996). Following Mester(1996)we use loan-loss provisions as a proportion of total loans as the output quality proxy.5We also use a variable to account for li-quidity risks because liquidity holdings(particularly those imposed by the authorities)represent a cost to bank that hold a higher proportion of cash and liquid assets have higher costs.As suggested in Hughes and Mester(1993)and Mester(1996)the level of equity capital,rather than the equity-to-assets ratio is included to control for di erences in risk preferences.6We also include a time5Berger and DeYoung(1997)argue that this variable may be a function of management e ciency,e cient banks will be better underwriters and monitors and hence will have lower losses, and hence it is endogenous,not exogenous.One referee also pointed out that a similar argument could be made for the liquidity risk variable,e cient mangers will hold only low levels of liquid assets,while ine cient mangers will hold excess amount of these low-yield assets.6As Mester(1996,p.1026)states,``Financial capital should be accounted for in the cost function and the level rather than the price of®nancial capital should be included since there is good reason to believe that cost-minimisation does not fully explain a bankÕs capital level±e.g.,regulations set minimum capital-to-assets ratios,and bank managers may be risk averse''.1610Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628trend in our cost frontier to capture the missing time dimension of inputs or other dynamics that are not modelled explicitly.7The cost frontiers are estimated using the random e ects panel data ap-proach(as in Lang and Welzel,1996).We use the panel data approach because technical e ciency is better studied and modelled with panels(See Baltagi and Gri n,1988;Cornwell et al.,1990;Kumbhakar,1993).The random e ects model is preferred over the®xed e ects model because the latter is considered to be the more appropriate speci®cation if we are focusing on a speci®c set of N ®rms.Moreover,and if N is large,a®xed e ects model would also lead to a substantial loss of degrees of freedom(See Baltagi,1995).Within sample scale economies are calculated as in Mester(1996)and are evaluated at the mean output,input price,quality and®nancial capital levels for the respective size quartiles.A measure of overall economies of scale(SE)is given by the following cost elasticity by di erentiating the cost function in Eq.(4)with respect to output.8This gives us:SE3i 1o ln TC o ln Q i3i 1a i123i 13j 1d ij ln Q j3i 13j 1q ij ln P i3i 1h i s ln El i3i 1 Àa i sin Z i b i cos Z i 2l i3i 13j 1Àa ij sin Z i Z jb i cos Z i Z j X 7 If SE`1then increasing returns to scale,implying economies of scale.If SE 1then constant returns to scale.If SE b1then decreasing returns to scale,implying diseconomies of scale. Following McKillop et al.(1996)and Lang and Welzel(1996)the rate of technical progress may be inferred from changes in a®rmÕs cost function over time.A time trend variable,T,serves as a proxy for disembodied technical change.The time-trend is aÔcatch-allÕvariable that captures the e ects of7One referee suggested that because annual economic conditions are not controlled for in the cost function speci®cations the time trend will capture more than just technological factors.Ideally one should control for exogenous conditions that change over time(e.g.economic indicators, competition,®nancial regulations).To this end a method suggested by DeYoung and Hasan(1998) was recommended where non-performing loans were decomposed into two components,exogenous and internal.Unfortunately data limitations did not allow us to undertake such a breakdown. 8Evano and Israilevich(1995)make the distinction between scale elasticity and scale e ciency where the former is measured as in Eq.(7),and the latter measures the change in output required to produce at minimum e cient scale.Throughout this paper references to economies and diseconomies of scale relate to scale elasticities.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281611technological factors:i.e.learning by doing and organisational changes al-lowing for the more e cient use of existing inputs,together with the e ects of other factors,such as changing environmental regulations(see Baltagi and Gri n,1988;Nelson,1984).Technical progress allows the®rm to produce a given output,Q,at lower levels of total cost over time,holding input prices and regulatory e ects constant.In order to estimate the impact of technical change we calculate the variation in the total cost due to a given change in technology. This can be measured by the partial derivative of the estimated cost function with respect to the time trend(T)and can be shown as follows:T C o ln TCo Tt1 t11T X 8The parameters on Eq.(8)capture the pure e ect of technical change,that is the decline in costs,keeping constant input proportions.93.Data and resultsOur data comprise the population of Japanese commercial banks listed in the London based IBCA bank credit rating agencies Bankscope(1997)dat-abase for the years1993±1996,and consists of139banks for each year from 1993to1995and136in1996.10The median asset size of banks included was Yen1.6trillion and the average asset size was Yen5trillion(see Appendix A for more details).Table1provides the descriptive statistics for the input, output and control variables for1996.This shows that for1996the median bank had Yen1.19trillion in loans,Yen334billion in securities and Yen41 billion of o -balance sheet items.Non-performing loans as a proportion of gross loans ranged between0.29%and9.5%,the latter®gure perhaps sug-gesting that some banks faced substantial credit quality problems. Various structural tests were undertaken to test for data poolability and heteroscedasticity and the results of these are shown in Table2.Homosce-dasticity,which implies the disturbance variance is constant across observa-tions,is not rejected at the one percent level for the whole sample applying the Goldfeld and Quandt,(1965)test.11The question of whether to pool the data9As in Lang and Welzel(1996),we do not include the interactive terms of outputs and input prices.Hence we are not able to measure the technical change associated with changes in output (scale augmenting in our estimates of technical change)and the technical change with the use of inputs due to changes in input prices.10The data set includes commercial bank only and excludes long-term credit banks and trust bank.11WhiteÕs(1980)test was also undertaken to investigate cross-sectional heteroscedasticity and we could not reject the hypothesis of homoscedasticity at the1%level of signi®cance.1612Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628or not naturally appears with panel data.In the econometric model,we assume that estimated parameters are the same over time.However,this assumption can be tested using Chow Õs (1960)test.Table 2shows that Chow Õs test forTable 1Descriptive statistics of the outputs,inputs and control variables used in the model,1996a Variable DescriptionMean Median St.Dev.Min MaxTC Total cost (YEN bil)165.740.8506.9 4.14291.5P 1Price of labour (YEN bil)(total personnel expenses/total asset)0.00890.00910.00230.00010.0142P 2Price of funds (%)(total interest expenses/total funds)0.01180.01010.00670.00510.0579P 3price of physical capital (%)(total depreciation and othercapital expenses/total ®xed assets)0.32470.27200.20140.18420.9419Q 1Total loans (domestic loans,foreign loans and trust a/c loans)(YEN bil)3373.01186.07903.098.046,887.0Q 2total securities (trading securities,Japanese public bonds,other investments and equity investments)(YEN bil)1189.0334.03005.032.023,098.0Q 3O balance sheet Items (contin-gent liabilities,acceptances,guarantees and L/Cs)(YEN bil)297.941.11029.9 1.55820.4Etotal equity (YEN bil)179.158.7417.3 4.62855.0NPL/L Non-performing loans/total loans (%)2.40 1.89 1.780.299.54L/TA Cash and due from banks/total assets (%) 4.293.62 2.630.8315.22TTime trend±±±19931996aNumber of observed banks:136.Table 2Structural test results Test performed Test statistics Degrees of freedom Critical value Decision Goldfeld±Quandt Test Hetroscedasticity 1.110n 1 382,n 2 170F 0X 01 n 1Àk Y n 2Àk 1X 250Rejected Poolability1.0023k 150Y N À4k 353F 0X 01 150Y 353 1X 00Not-rejected Translog form55.689k 18v 20X 05 28X 869Rejected No risk and quality variables91.144k 9v 20X 05 16X 916Rejected No equity variables 87.288k 7v 20X 05 14X 067Rejected No NPL/L variables 15.510k 1v 20X 05 3X 842Rejected No L/TA variables 3.333k 1v 20X 05 3X 842Not-rejected No technical progress41.022k 2v 20X 055X 991RejectedY.Altunbas et al./Journal of Banking &Finance 24(2000)1605±162816131614Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628 poolability over time yields an F-value of1.002which is distributed as F(150, 353)under the null hypothesis:H0X b t b for t 1Y F F F Y T,and this test does not reject poolability across time periods.We also undertake likelihood ratio tests,as an alternative to the F-statistic for testing hypotheses about s,k1and k2(see Greene,1993b),to see if the cost function that included the risk and quality variables(RQCF)di ered signi®-cantly from the standard model(CF).The likelihood ratio test rejects the hypothesis that the two models CF and RQCF are not signi®cantly di erent. Similar tests were also undertaken to see whether the inclusion of individual risk and quality variables as well as the time trend signi®cantly altered the model.Table2shows the likelihood ratio statistics indicating that all but the L/TA variables have a signi®cant in¯uence on model speci®cation.This sug-gests that the equity and non-performing loans variables provide the bulk of information relating to quality and risk factors.Table3shows the estimated scale,X-ine ciencies and technical change results(parameter estimates are given in Appendix A).The®ndings from the RQCF model which controls for risk and quality factors con¯ict with the re-sults from previous studies on Japanese banking in that we®nd scale econo-mies to be much smaller.For instance,McKillop et al.(1996)®nd evidence of ÔappreciableÕscale economies in their study using data from the®ve largest Japanese banks,and their results support the earlier®ndings of Kasuya(1986), Tachibanaki et al.(1991)and Fukuyama(1993).Our results show that dis-economies of scale become much more widespread and optimal bank size falls from around Yen5±10trillion to Yen1±2trillion when risk and quality factors are taken into account.Estimates of scale economies for the largest Japanese commercial banks tend to be overstated when the underlying cost function speci®cation does not control for these factors.This®nding also contrasts with the studies by Hughes et al.(1995)and McAllister and McManus(1993)on US banks which®nd that either optimal bank size increases or scale economies are never exhausted when risk and quality variable included.The con¯icting results could be related to a variety of factors including:di erent institutional struc-tures,the decline in capital strength of Japanese banks during the1990s;the di erent time frame covered and growth variation in the output/input mix of Japanese compared with US banks.Unlike Clark(1996)who®nds that risk variables signi®cantly alter X-inef-®ciency estimates for US banks,we®nd that in the case of Japanese banks the ine ciency results from both models are similar.Mean levels of ine ciency range between5%and7%,with no discernible trend across size classes.This suggests that if the average bank in each size class used its inputs as e ciently as possible it could decrease its costs somewhere in the region of5±7%.These X-ine ciency scores are similar to the results found in recent US studies(see Berger and DeYoung(1997)and Berger and Humphrey(1997)).Overall the results from the model which controls for risk and quality factors(RQCF)Table3Scale economies,ine ciencies and technical change for Japanese commercial banks1993±1996aTotal assets sizes(Yen bil)1993199419951996 RQCF CF RQCF CF RQCF CF RQCF CFScale economies b1±5000.773Ã0.9810.774Ã0.9830.769Ã0.9900.774Ã0.991 500±10000.889Ã0.949Ã0.885Ã0.944Ã0.879Ã0.945Ã0.875Ã0.947Ã1000±20000.9810.946Ã0.9780.946Ã0.9780.949Ã0.9770.948Ã2000±3000 1.050ÃÃ0.965ÃÃ 1.050ÃÃ0.967ÃÃ 1.0440.961ÃÃ1.0440.964Ã3000±5000 1.091Ã0.934Ã 1.093Ã0.938Ã 1.090Ã0.936Ã 1.086Ã0.932Ã5000±10,000 1.212Ã 1.008 1.210Ã 1.000 1.204Ã0.995 1.196Ã0.999 >10,000 1.457Ã 1.063ÃÃ 1.455Ã 1.063ÃÃ 1.455Ã 1.072Ã 1.456Ã 1.081ÃScale ine ciency c1±5000.2230.0780.2630.0970.2330.0830.1940.029 500±10000.1660.1710.1500.1930.1500.2020.1510.166 1000±20000.0000.1530.0000.1720.0000.1340.0000.125 2000±30000.0450.1680.0670.1450.0650.0830.0780.081 3000±50000.0690.2040.0800.1640.0720.1690.0720.102 5000±10,0000.2340.0000.2150.0000.1750.0000.1340.000 >10,0000.2970.2290.2540.2250.2490.2400.2590.251 Ine ciency scores1±5000.0730.0650.0720.0650.0690.0630.0740.070 500±10000.0550.0460.0560.0470.0530.0410.0710.053 1000±20000.0470.0430.0500.0500.0530.0470.0600.055 2000±30000.0490.0450.0600.0580.0640.0550.0680.064 3000±50000.0510.0460.0640.0580.0610.0510.0760.059 5000±10,0000.0560.0670.0700.0810.0530.0530.0370.045 >10,0000.0760.0600.0850.0690.0610.0490.0930.086 All0.0560.0500.0610.0570.0580.0500.0680.060Overalltechnicalprogress d)0.040Ã)0.046Ã)0.026Ã)0.031Ã)0.012Ã)0.016Ã0.002)0.001ÃFor the scale economy estimates,statistically di erent from one at the one percent level for two-tailed test for the scale results,for the technical progress estimates statistically di erent from zero at the one percent level.ÃÃFor values signi®cantly di erent from one at the10%level.a Results reported in the table are derived from estimated coe cients for a single equation panel data model1993±1996.Estimates calculated for the mean values within each size category.b The scale economies measure is SE o ln TC a o ln Q1 o ln TC a o ln Q2 o ln TC a o ln Q3 where TC is the actual cost of producing the average output bundle at the average input prices,®nancial capital and quality factors;Q i is the volume of output i.SE`1indicates increasing re-turns to scale;SE b1indicates decreasing returns to scale;SE 1indicates constant returns to scale.c The scale ine ciency measure is derived from the methodology suggested by Evano and Israi-levich(1995).d Overall technical progress can be measured as the elasticity of total cost TC with respect to time t, i.e.,T C o lnTC a o T.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281615。

A multi-product multi-echelon inventory control model with joint replenishment strategy

A multi-product multi-echelon inventory control model with joint replenishment strategyWei-Qi Zhou ⇑,Long Chen,Hui-Ming GeSchool of Automobile and Trafﬁc Engineering,Jiangsu University,Zhenjiang 212013,Chinaa r t i c l e i n f o Article history:Received 23January 2011Received in revised form 11April 2012Accepted 21April 2012Available online xxxx Keywords:InventoryMulti-product Multi-echelonGenetic Algorithm (GA)Joint replenishment strategya b s t r a c tOn the basis of analyzing the shortages of present studies on multi-echelon inventory con-trol,and considering some restrictions,this paper applies the joint replenishment strategy into the inventory system and builds a multi-product multi-echelon inventory control model.Then,an algorithm designed by Genetic Algorithm (GA)is used for solving the model.Finally,we respectively simulate the model under three different ordering strate-gies.The simulation result shows that the established model and the algorithm designed by GA have obvious superiority on reducing the total cost of the multi-product multi-echelon inventory system.Moreover,it illustrates the feasibility and the effectiveness of the model and the GA method.Crown Copyright Ó2012Published by Elsevier Inc.All rights reserved.1.IntroductionA supply chain is a network of nodes cooperating to satisfy customers’demands,and the nodes are arranged in echelons.In the network,each node’s position is corresponding to its relative position in reality.The nodes are interconnected through supply–demand relationships.These nodes serve external demand which generates orders to the downstream echelon,and they are served by external supply which responds to the orders of the upstream echelon.The problem of multi-echelon inventory control has been investigated as early as the 1950s by researchers such as Arrow et al.[1]and Love [2].The main challenge in these problems is to control the inventory levels by determining the size of the orders for each echelon during each period so as to optimize a given objective function.Many researchers have studied how to reduce the inventory cost of either suppliers or distributors,or have considered either the distribution system or the production system.Burns and Sivazlian [3]investigated the dynamic response of a multi-echelon supply chain to various demands placed upon the system by a ﬁnal consumer.Van Beek [4]carried out a model in order to compare several alternatives for the way in which goods are forwarded from factory,via stores to the cus-tomers.Zijm [5]presented a framework for the planning and control of the materials ﬂow in a multi-item production system.The prime objective was to meet a presanctiﬁed customer service level at minimum overall costs.Van der Heijden [6]deter-mined a simple inventory control rule for multi-echelon distribution systems under periodic review without lot sizing.Yoo et al.[7]proposed an improved DRP method to schedule multi-echelon distribution network.Diks and Kok [8]considered a divergent multi-echelon inventory system,such as a distribution system or a production system.Andersson and Melchiors [9]considered a one warehouse several retailers’inventory system,assuming lost sales at the retailers.Huang et al.[10]0307-904X/$-see front matter Crown Copyright Ó2012Published by Elsevier Inc.All rights reserved./10.1016/j.apm.2012.04.054⇑Corresponding author.Tel.:+8651188780074;fax:+8651188791900.E-mail address:zwqsky@ (W.-Q.Zhou).2W.-Q.Zhou et al./Applied Mathematical Modelling xxx(2012)xxx–xxxconsidered a one-warehouse multi-retailer system under constant and deterministic demand,which is subjected to transpor-tation capacity for every delivery godimos and Koukoumialos[11]developed closed-form customer service models.And many researchers have modeled an inventory system of only two-echelon or two-layer.Gupta and Albright[12] modeled a two-echelon multi-indentured repairable-item inventory system.Axsäter and Zhang[13]considered a two-level inventory system with a central warehouse and a number of identical retailers.Axsäter[14]considered a two-echelon distri-bution inventory system with stochastic demand.Chen et al.[15]considered a two-level inventory system in which there are one supplier and multiple retailers.Tee and Rossetti[16]developed a simulation model to explore the model’s ability to pre-dict system performance for a two-echelon one-warehouse,multiple retailer system.Seferlis and Giannelos[17]developed a new two-layered optimization-based control approach for multi-product,multi-echelon supply chain networks.Hill et al.[18]considered a single-item,two-echelon,continuous-review inventory model.Al-Rifai and Rossetti[19]presented a two-echelon non-repairable spare parts inventory system.Mitra[20]considered a two echelon system with returns under more generalized conditions,and developed a deterministic model as well as a stochastic model under continuous review for the system.There are also many researches on multi-echelon inventory control,considering either the distribution system or the sup-ply system.Choi et al.[21]evaluated conventional lot-sizing rules in a multi-echelon coalescence MRP system.Chikán and Vastag[22]described a multi-echelon production inventory system and developed a heuristic suggestion.Bregman et al.[23]introduced a heuristic algorithm for managing inventory in a multi-echelon environment.Van der Vorst et al.[24]pre-sented a method for modeling the dynamic behavior of multi-echelon food supply chains and evaluating alternative designs of the supply chain by applying discrete-event simulation.The model considered a producer,a distribution center and2re-tailer outlets.Iida[25]studied a dynamic multi-echelon inventory problem with nonstationary u and Lau[26] applied different demand-curve functions to a simple inventory/pricing model.Routroy and Kodali[27]developed a three-echelon inventory model for single product,which consists of single manufacturer,single warehouse and single retailer. Dong and Lee[28]considered a multi-echelon serial periodic review inventory system and3echelons for numerical exam-ple.The system extended the approximation to the time correlated demand process of Clark and Scarf[29],and studied in particular for an auto-regressive demand model the impact of leadtimes and auto-correlation on the performance of the se-rial inventory system.Gumus and Guneri[30]structured an inventory management framework and deterministic/stochas-tic-neurofuzzy cost models within the context of this framework for effective multi-echelon supply chains under stochastic and fuzzy environments.Caggiano et al.[31]described and validated a practical method for computing channelﬁll rates in a multi-item,multi-echelon service parts distribution system.Yang and Lin[32]provided a serial multi-echelon integrated just-in-time(JIT)model based on uncertain delivery lead time and quality unreliability considerations.Gumus et al.[33] structured an inventory management framework and deterministic/stochastic-neuro-fuzzy cost models within the context of the framework.Then,a numerical application in a three-echelon tree-structure chain is presented to show the applicabil-ity and performance of proposed framework.The model only handled one product type.Only one other paper we are aware of addresses a problem similar to ours and consideres inventory optimization in a multi-echelon system,considering both the distribution system and the supply system.Rau et al.[34]developed a multi-echelon inventory model for a deteriorating item and to derive an optimal joint total cost from an integrated perspective among the supplier,the producer,and the buyer.The model considered the single supplier,single producer and single buyer. The basic difference between our model and Rau et al.[34]is that our model considers multiple suppliers,one producer,and multiple distributors and buyers.Additionally,an algorithm designed by Genetic Algorithm(GA)is used for solving the mod-el,and we apply the joint replenishment strategy into the model.The remainder of this paper is organized as follows:In Section2,the various assumptions are made and the multi-product multi-echelon inventory control model is developed.In Section3,GA is used for solving the model and the algorithm based on GA is designed.Then,we simulate the model under three different ordering strategies,respectively.In Section4,conclu-sions and limitations in this research are presented.2.Mathematical model2.1.The multi-product multi-echelon inventory control model descriptionIn this model,the raw materials,accessories or products can be supplied from the nodal enterprise of layer k to the nodal enterprise of layer k +1,but there is no logistics between nodal enterprises of the same layer or the non-adjacent layers.And also there is no reverse logistics from the nodal enterprise of high-layer to the nodal enterprise of low-layer.The multi-prod-uct multi-echelon inventory system is divided into three subsystems (supply network,core enterprise and distribution net-work)by the core enterprise as a dividing line (Fig.1).The key issue to the multi-product multi-echelon inventory system is to determine the optimal order quantity and the optimal order cycle for each nodal enterprise in order to minimize the inventory cost of the whole system.In this paper,the (T ,S )inventory control strategy based on multi-product joint replenishment is used.The multi-product joint replenishment strategy is an ordering strategy that to order varieties of products in one order cycle.Each nodal enter-prise determines a minimum order cycle as the basic order cycle,and the order cycle of the same enterprise to order each product is an integral multiple of the basic order cycle.2.2.Assumptions(1)In this supply chain,there is only one core enterprise.(2)Allow a variety of products,but the price of each product is ﬁxed.And also allow a variety of raw materials or acces-sories,but one supplier only provides one raw material or accessory.(3)The demand of each nodal enterprise per day is random,but it obeys Poisson distribution.(4)Lead time of each nodal enterprise is ﬁxed.(5)Storage cost per product per unit time is constant.And the storage cost of different nodal enterprises is allowed to bedifferent.2.3.Notations P w price of product w (there are W kind of products,and w =1,2,...,W )P g k Àl price of raw material or accessory provided by the nodal enterprise g of layer k Àl (g =1,2,...,m k Àl ;l =1,2,...,k À1;m k Àl is the number of nodal enterprises of layer k Àl)T h k basic order cycle of the nodal enterprise h of layer k to order products from the nodal enterprises of layer k À1T ðg ;h Þk order cycle of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1Z ðg ;h Þkratio of T ðg ;h Þkand T h k ,which is a positive integer,so T ðg ;h Þk¼Z ðg ;h ÞkT hkA h k public ordering cost of the nodal enterprise h of layer k to order products from the nodal enterprises of layer k À1ineach order cycle,which is independent of the order quantity and the order varietiesA ðg ;h Þkindividual ordering cost of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1in each order cycle,which is dependent of the order quantity and the order varietiesA ðh ;i ;w Þk þl individual ordering cost of the nodal enterprise i of layer k +l to order the product w from the nodal enterprise h of layer k +l À1in each order cycle,in the distribution networkT i k þl basic order cycle of the nodal enterprise i of layer k +l to order products from the nodal enterprises of layer k +l À1,in the distribution networkT ði ;w Þk þl order cycle of the nodal enterprise i of layer k +l to order product w from the nodal enterprises of layer k À1,in the distribution networkZ ði ;w Þk þlratio of T ði ;w Þk þl and T i k þl ,which is a positive integer,so T ði ;w Þk þl ¼Z ði ;w Þk þl T i k þlS ðg ;h Þk maximum inventory level of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1E D ðg ;h Þk average demand of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1perdayL ðg ;h Þk lead time of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1L ði ;w Þk þl the average lead time of the nodal enterprise i of layer k +l to order the product w from the nodal enterprise of layer k +l À1H ðg ;h Þk storage cost of the nodal enterprise h of layer k per product per yearY ðg ;h Þk quantity demand of the nodal enterprise h of layer k to order products from the nodal enterprise g of layer k À1peryear,so Y ðg ;h Þk ¼365E D ðg ;h Þkn ðg ;h Þkthe number of trips from the nodal enterprise g of layer k À1to the nodal enterprise h of layer k per year,which isinversely proportional to order cycle,so n ðg ;h Þk ¼Z ðg ;h Þk T h kÀ1W.-Q.Zhou et al./Applied Mathematical Modelling xxx (2012)xxx–xxx3f ðg ;h Þkﬁxed transportation cost from the nodal enterprise g of layer k À1to the nodal enterprise h of layer k in each trans-portation (such as driver’s wage)t ðg ;h Þkvariable transportation cost to transport the unit product from the nodal enterprise g of layer k À1to the nodal enter-prise h of layer k (such as cost of fuels),which is the function of transport efﬁciency and order quantity in the case of ﬁxed transportation distanceX ðh ;i ;w Þkthe expected value of the produce w of the nodal enterprise h of layer k relative to order quantity of the nodal enter-prise i of layer k +11ðg ;h ;w Þk conversion rate of product w produced by the nodal enterprise h of layer k relative to raw materials or accessories supplied by the nodal enterprise g of layer k À1g ðh ;i ;w Þksupply coefﬁcient of product w supplied from the nodal enterprise h of layer k to the nodal enterprise i of layer k +1,and P m k þ1i ¼1g ðh ;i ;w Þk ¼1b ðg ;h ;w Þkproportionality coefﬁcient of raw materials or accessories used to produce product w ,which are supplied from thenodal enterprise g of layer k À1to the nodal enterprise h of layer k ,and P W w ¼1b ðg ;h ;w Þk¼1B ðh ;i ;w Þkshortage penalty per produce w per order cycle from the nodal enterprise i of layer k +1to the nodal enterprise h of layer k2.4.Multi-product multi-echelon inventory control modelWe divide the inventory cost into ordering cost,holding cost,transportation cost and shortage cost.(1)Ordering costThe total ordering cost of the core enterprise per year is deﬁned as follows:C Order C¼X m kh ¼1A h kT hkþXm k À1g ¼1X m k h ¼1A ðg ;h ÞkZ ðg ;h ÞkT hk:ð1ÞThe total ordering cost of the supply network per year is deﬁned as follows:C Order S¼X k À2l ¼1X m k Àl g ¼1Ag k ÀlT g k ÀlþX k À2l ¼1X m k Àl À1f ¼1X m k Àl g ¼1A ðf ;g Þk Àl Z ðf ;g Þk Àl T g k Àl:ð2ÞThe total ordering cost of the distribution network per year is deﬁned as follows:C Order D¼X N Àk l ¼1X m k þl i ¼1Ai k þl T ik þlþX N Àk l ¼1X m k þl À1h ¼1X m k þl i ¼1X W w ¼1A ðh ;i ;w Þk þl Z ði ;w Þk þl T ik þl:ð3ÞTherefore,the total ordering cost of the multi-product multi-echelon inventory system per year is deﬁned as follows:TC Order ¼C Order C þC Order S þC Order D:ð4Þ(2)Holding costThe inventory level of the nodal enterprise h of layer k when it has received the order quantity from the nodal enter-prise of layer k À1is:S ðg ;h ÞkÀE D ðg ;h Þk L ðg ;h Þk ;ð5Þand the inventory level of the nodal enterprise h of layer k before it receives the order quantity next order cycle is:S ðg ;h ÞkÀE D ðg ;h Þk L ðg ;h Þk ÀE D ðg ;h Þk Z ðg ;h Þk T h k :ð6ÞTherefore,the average inventory level in one order cycle is:12S ðg ;h Þk ÀE D ðg ;h Þk L ðg ;h Þk þS ðg ;h Þk ÀE D ðg ;h Þk L ðg ;h Þk ÀE D ðg ;h Þk Z ðg ;h Þk T h k hi ¼S ðg ;h Þk ÀE D ðg ;h Þk L ðg ;h Þk ÀE D ðg ;h ÞkZ ðg ;h Þk T h k 2:ð7ÞThe total holding cost of the core enterprise per year is deﬁned as follows:C Hold C¼Xm k À1g ¼1X m k h ¼1S ðg ;h Þk ÀE D ðg ;h Þk L ðg ;h Þk ÀE D ðg ;h Þk Z ðg ;h Þk T h k22435H ðg ;h Þk:ð8Þ4W.-Q.Zhou et al./Applied Mathematical Modelling xxx (2012)xxx–xxxAs a practical matter,we must ensure that the average inventory level is greater than zero,as shown in Eq.(9):Sðg;hÞk ÀE Dðg;hÞkLðg;hÞkÀE Dðg;hÞkZðg;hÞkT hk2>0:ð9ÞThe total holding cost of the supply network per year is deﬁned as follows:C Hold S ¼X kÀ2l¼1Xm kÀlÀ1f¼1X m kÀlg¼1Sðf;gÞkÀlÀE Dðf;gÞkÀlLðf;gÞkÀlÀE Dðf;gÞkÀlZðf;gÞkÀlT gkÀl22435Hðf;gÞkÀl;ð10Þunder the following constraint:Sðf;gÞkÀl ÀE Dðf;gÞkÀlLðf;gÞkÀlÀE Dðf;gÞkÀlZðf;gÞkÀlT gkÀl2>0:ð11ÞThe total holding cost of the distribution network per year is deﬁned as follows:C HoldD ¼X NÀkl¼1X m kþli¼1X Ww¼1Sði;wÞkþlÀE Dði;wÞkþlLði;wÞkþlÀE Dði;wÞkþlZði;wÞkþlT ikþl22435Hði;wÞkþl;ð12Þunder the following constraint:Sði;wÞkþl ÀE Dði;wÞkþlLði;wÞkþlÀE Dði;wÞkþlZði;wÞkþlT ikþl2>0:ð13ÞTherefore,the total holding cost of the multi-product multi-echelon inventory system per year is deﬁned as follows:TC Hold¼C HoldC þC HoldSþC HoldD:ð14Þ(3)Transportation costThe total transportation cost of the core enterprise per year is deﬁned as follows:C Trans C ¼Xm kÀ1g¼1X m kh¼1nðg;hÞkfðg;hÞkþtðg;hÞkYðg;hÞkh i:ð15ÞThe total transportation cost of the supply network per year is deﬁned as follows:C Trans S ¼X kÀ2l¼1Xm kÀlÀ1f¼1X m kÀlg¼1nðf;gÞkÀlfðf;gÞkÀlþtðf;gÞkÀl Yðf;gÞkÀlh i;ð16Þwhere nðf;gÞkÀl ¼Zðf;gÞkÀlT gkÀlÀ1;Yðf;gÞkÀl¼365E Dðf;gÞkÀlThe total transportation cost of the distribution network per year is deﬁned as follows:C TransD ¼X Ww¼1X NÀkl¼1Xm kþlÀ1h¼1X m kþli¼1nði;wÞkþlfðh;iÞkþlþtðh;iÞkþl Yðh;i;wÞkþlh i;ð17Þwhere nði;wÞkþl ¼Zði;wÞkþlT ikþlÀ1;Yðh;i;wÞkþl¼365E Dðh;i;wÞkþlTherefore,the total transportation cost of the multi-product multi-echelon inventory system per year is deﬁned as follows:TC Trans¼C TransC þC TransSþC TransD:ð18Þ(4)Shortage costAssuming Xðh;i;wÞk obeys Poisson distribution p kðh;i;wÞkZðg;hÞkT hkþLðg;hÞkh iduring the period Zðg;hÞkT hkþLðg;hÞk,so:Xðh;i;wÞk ¼X1u¼AuÀgðh;i;wÞk1ðg;h;wÞkbðg;h;wÞkSðg;hÞkp kðh;i;wÞkZðg;hÞkT hkþLðg;hÞkh i:ð19ÞThe total shortage cost of the core enterprise per year is deﬁned as follows:C Shortage C ¼X m kh¼1Xm kþ1i¼1X Ww¼1Bðh;i;wÞkXðh;i;wÞkZðg;hÞkT hk:ð20ÞW.-Q.Zhou et al./Applied Mathematical Modelling xxx(2012)xxx–xxx5The total shortage cost of the supply network per year is deﬁned as follows:C Shortage S¼X k À2l ¼1X m k Àl g ¼1X m k Àl þ1h ¼1B ðg ;h Þk Àl X ðg ;h Þk ÀlZ k Àl T g k Àl;ð21ÞwhereX ðg ;h Þk Àl¼P 1u ¼Au Àgðg ;h Þk Àl 1ðf ;g Þk Àl S ðf ;g Þk Àlp k ðg ;h Þk Àl Z ðf ;g Þk Àl T g k Àl þL ðf ;g Þk Àl h i ;g ðg ;h Þk Àl ¼E D ðg ;h Þk Àl þ1ÀÁP m k Àl þ1h ¼1E Dðg ;h Þk Àl þ1ÀÁ,and P m k Àl þ1h ¼1g ðg ;h Þk Àl ¼1.The total shortage cost of the distribution network per year is deﬁned as follows:C Shortage D¼X N Àk l ¼1X m k þl i ¼1X m k þl þ1j ¼1X W w ¼1B ði ;j ;w Þk þl X ði ;j ;w Þk þl Z ði ;w Þk þl T i k þl;ð22ÞwhereX ði ;j ;w Þk þl¼X 1u ¼Au Àg ði ;j ;w Þk þl S ði ;w Þk þl p k ði ;j ;w Þk þl Z ði ;w Þk þl T i k þl þL ði ;w Þk þl h i;gði ;j ;w Þk þl¼E D ði ;j ;w Þk þlk þl þ1j ¼1E D ði ;j ;w Þk þl;andX m k þl þ1j ¼1g ði ;j ;w Þk¼1:Therefore,the total shortage cost of the multi-product multi-echelon inventory system per year is deﬁned as follows:TC Shortage ¼C Shortage C þC Shortage SþC Shortage D :ð23ÞIn conclusion,we develop the multi-product multi-echelon inventory control model as follows:minTC ¼TC Order þTC Hold þTC Trans þTC Shortage ;ð24Þs :t :E D ðg ;h ÞkL ðg ;h Þk þE D ðg ;h Þk Z ðg ;h Þk T h k 2ÀS ðg ;h Þk <0;ð25ÞE D ðf ;g Þk Àl L ðf ;g Þk Àl þE D ðf ;g Þk Àl Z ðf ;g Þk Àl T g k Àl 2ÀS ðf ;g Þk Àl <0;l ¼1;2;...;k À2;f ¼1;2;...;m k Àl À1;g ¼1;2;...;m k Àl ;ð26ÞE D ði ;w Þk þl L ði ;w Þk þl þE D ði ;w Þk þl Z ði ;w Þk þl T i k þl2ÀS ði ;w Þk þl <0;l ¼1;2;...;N Àk ;i ¼1;2;...;m k þl ;w ¼1;2;...;W ;ð27Þmin Z g ¼1;h ðÞk ;Z g ¼2;h ðÞk ;...;Z g ¼m k À1;h ðÞk h i¼1;ð28Þmin Z ðf ¼1;g Þk Àl ;Z ðf ¼2;g Þk Àl ;...;Z ðf ¼m k Àl À1;g Þk Àl h i¼1;l ¼1;2;3;...;k À2;ð29Þmin Z ði ;w ¼1Þk þl ;Z ði ;w ¼2Þk þl ;...;Z ði ;w ¼W Þk þl h i ¼1;l ¼1;2;3;...;N Àk :ð30Þ(28)–(30)can ensure that at least one product’s order cycle is the basic order cycle.The decision variables in the model are allintegers greater than or equal to zero.3.Simulation and analysis 3.1.Simulation model based on GAThe objective function of this optimization model is minimization,and the objective function of GA is maximization,so the objective function of this optimization model cannot be taken as the ﬁtness function of GA.We must convert the objec-tive function to the ﬁtness function of GA as follows:F ðX Þ¼TC max ÀTC ;TC <TC max ;0;TC P TC max ;&ð31Þwhere F (X )is the individual ﬁtness.TC max is a relatively large number,and in this simulation model,we may put TC max as the largest objective function value during evolution.The multi-product multi-echelon inventory control model can be reduced to a nonlinear programming problem as follows:6W.-Q.Zhou et al./Applied Mathematical Modelling xxx (2012)xxx–xxxmin f ðX Þ;ð32Þs :t :g i ðX Þ60ði ¼1;2;3;...;m Þ:In this paper,penalty function is used as constraint.So,we construct the penalty function as follows:/ðX ;c kÞ¼X m i ¼1c k i min g i ðX Þ;0ðÞ2;ð33Þwhere k is iteration times of GA.c k i is penalty factor,which is a monotone increasing sequence and positive value.Andc k þ1i ¼e i Ác ki .The experience in computation shows that if c k i ¼1and e i =5À10,we can achieve satisfactory results.So,we change (31)to the function as follows:F ðX Þ¼TC max ÀTC À/ðX ;c k Þ;TC <TC max ;0;TC P TC max :(ð34ÞMoreover,we use the ﬂoating point number coding (the chromosome’s length equals the number of decision variables),the roulette wheels selection mechanism as the selection operator,the arithmetic cross technique as the crossover operator,the Gauss mutation operator as the mutation operator,and algebra (its values range from 100to 500)as the termination criteria.3.2.SimulationAs an illustration,we develop a multi-product multi-echelon inventory control model which has four suppliers (the four suppliers are divided into two levels and each level has two suppliers),one core enterprise and two distributors,and has two products (Fig.2).The average demand of the customers to order product 1and product 2from the distributor 1of layer 4per day is 6units and 3units.The average demand of the customers to order product 1and product 2from the distributor 2of layer 4per day is 4units and 7units.The values of other parameters are shown in Tables 1–3.Table 2The values of the parameters of the supply network.Parameters A 12A ð1;1Þ2A ð2;1Þ2A 22A ð1;2Þ2A ð2;2Þ2L ð1;1Þ2L ð2;1Þ2L ð1;2Þ2Values $70$200$180$60$250$250666Parameters L ð2;2Þ2H ð1;1Þ2H ð2;1Þ2H ð1;2Þ2H ð2;2Þ2f ð1;1Þ2f ð2;1Þ2f ð1;2Þ2f ð2;2Þ2Values 6$3$6$3$15$200$140$250$150Parameters t ð1;1Þ2t ð2;1Þ2t ð1;2Þ2t ð2;2Þ2g ð1;1Þ2g ð2;1Þ2g ð1;2Þ2g ð2;2Þ21ð1;1Þ2Values $4$6$5$811111Parameters 1ð2;1Þ21ð1;2Þ21ð2;2Þ2B ð1;1Þ2B ð2;1Þ2B ð1;2Þ2B ð2;2Þ2Values0.510.5$150$120$160$140Table 1The values of the parameters of the core enterprise.Parameters A 13A ð1;1Þ3A ð2;1Þ3L ð1;1Þ3L ð2;1Þ3H ð1;1Þ3H ð2;1Þ3f ð1;1Þ3f ð2;1Þ3Values $100$240$32055$5$40$300$350Parameters t ð1;1Þ3t ð2;1Þ3g ð1;1;1Þ3g ð1;2;1Þ3g ð1;1;2Þ3g ð1;2;2Þ31ð1;1;1Þ31ð2;1;1Þ31ð1;1;2Þ3Values $15$100.60.40.30.70.510Parameters 1ð2;1;2Þ3b ð1;1;1Þ3b ð1;1;2Þ3b ð2;1;1Þ3b ð2;1;2Þ3B ð1;2;1Þ3B ð1;1;2Þ3B ð1;2;2Þ3B ð1;1;1Þ3Values110.50.5$150$120$180$200W.-Q.Zhouet al./Applied Mathematical Modelling xxx (2012)xxx–xxx 7。

ACCA P5 Summary

1Introduction to strategic management accounting1.1I ntroduction to planning, control and decision making☞Strategic planning is the process of deciding on objectives of the organization, on changes in these objectives, on the resource to attain these objectives, and on the policies that are to govern the acquisition, use and disposition of these resources.☞Characteristics of strategic information⏹Long term and wide scope⏹Generally formulated in writing⏹Widely circulated广泛流传⏹Doesn’t trigger direct action, but series of lesser plans⏹Includes selection of products, purchase of non-current assets, required levels ofcompany profit☞Management control: the process by which management ensure that resources are obtained and used effectively and efficiently in the accomplishment of the organisation’s objectives. It is sometimes called tactics ad tactical planning.☞Characteristics of management accounting information⏹Short-term and non-strategic⏹Management control planning activities include preparing annual sales budget⏹Management control activities include ensuring budget targets are reached⏹Carried out in a series of routine and regular planning and comparison procedures⏹Management control information covers the whole organisation, is routinely collected,is often quantitative and commonly expressed in money terms (cash flow forecasts, variance analysis reports, staffing levels⏹Source of information likely to be endogenous内生的☞Characteristics of operational control⏹Short-term and non-strategic⏹Occurs in all aspects of an organisations activities and need for day to dayimplementation of plans⏹Often carried out at short notice⏹Information likely to have an endogenous source, to be detailed transaction data,quantitative and expressed in terms of units/hours⏹Includes customer orders and cash receipts.1.2Management accounting information for strategic planning and control☞Strategic management accounting is a form of management accounting in which emphasis is placed on information about factors which are external to the organisation, as well as non-financial and internally-generated information.⏹External orientation: competitive advantage is relative; customer determination⏹Future orientation: forward- and outward looking; concern with values.⏹Goal congruence: translates the consequences of different strategies into a commonaccounting language for comparison; relates business operations to financial performance.1.3Planning and control at strategic and operational levels☞Linking strategy and operations, if not: unrealistic plans, inconsistent goals, poor communication, inadequate performance measurement.1.3.1Strategic control systems☞Formal systems of strategic control:⏹strategy review;⏹identify milestones of performance( outline critical success factors, short-term stepstowards long-term goals, enables managers to monitor actions)⏹Set target achievement levels (targets must be reasonably precise, suggest strategiesand tactics, relative to competition)⏹Formal monitoring of the strategic process⏹Reward.☞Desired features of strategic performance measures⏹Focus on what matters in the long term⏹Identify and communicate drivers of success⏹Support organisational learning⏹Provide a basis for reward⏹Measurable; meaningful; acceptable;⏹Described by strategy and relevant to it⏹Consistently measured⏹Re-evaluated regularly1.4Benchmarking1.4.1Types of benchmarking☞Internal benchmarking: easy; no innovative or best-practice.☞Industry benchmarking:⏹Competitor benchmarking: difficult to obtain information⏹Non-competitor benchmarking: motivate☞Functional benchmarking: find new, innovative ways to create competitive advantage1.4.2Stages of benchmarking☞Set objectives and determine the area to benchmark☞Establish key performance measures.☞Select organizations to study☞Measure own and others performance☞Compare performance☞Design and implement improvement prgoramme☞Monitor improvements1.4.3Reasons for benchmarking☞Assess current strategic position☞Assess generic competitive strategy☞Spur to innovation☞Setting objectives and targets☞Cross comparisons☞Implementing change☞Identifies the process to improve☞Helps with cost reduction, or identifying areas where improvement is required☞Improves the effectiveness of operations☞Delivers services to a defined standard☞Provide early warning of competitive disadvantage1.4.4Disadvantages of benchmarking☞Implies there is one best way of doing business☞Yesterday’s solution to tomorrow’s problem☞Catching-up exercise rather than the development of anything distinctive☞Depends on accurate information about comparator companies☞Potential negative side effects of ‘what gets measured gets done’.2Performance management and control of the organization2.1Strengths and weaknesses of alternative budget models2.1.1Incremental budgeting☞Is the traditional approach to setting a budget and involves basing next year’s budget on the current year’s results plus an extra amount for estimated growth of inflation next year. ☞Strengths: easy to prepare; can be flexed to actual levels to provide more meaningful control information☞Weaknesses: does not take account of alternative options; does not look for ways of improving performance; only works if current operations are as effective, efficient and economical as they can be; encourage slack in the budget setting process.2.1.2Zero based budgeting☞Preparing a budget for each cost centre from scratch.☞Strengths:⏹Provides a budgeting and planning tool for management that responds to changes inthe business environment.⏹Requires the organization to look very closely at its cost behavior patterns, andimproves understanding of cost-behaviour patterns.⏹Should help identify inefficient or obsolete processes, and thereby also help reducecosts.⏹Results in a more efficient allocation of resources⏹Be particularly useful in not-for-profit organizations which have a focus on achievingvalue for money.☞Weaknesses:⏹Requires a lot of management time and effort⏹Requires training in the use of ZBB techniques so that these are applied properly⏹Questioning current practices and processes can be seen as threatening2.1.3Rolling budgets☞Continuously updated by adding a further period when the earliest period has expired.☞Strengths:⏹Reduce the uncertainty of budgeting for business operating in an unstableenvironment. It is easier to predict what will happen in the short-term.⏹Most suitable form of budgeting for organizations in uncertain environments, wherefuture activity levels, costs or revenues cannot be accurately foreseen.⏹Planning and control is based on a more recent plan which is likely to be morerealistic an more relevant than a fixed annual budget drawn up several months ago.⏹The process of updating the budget means that managers identify current changes( and so can respond to these changes more quickly)⏹More realistic targets provide a better basis on which to appraise managers’performance⏹Realistic budgets are likely to have a better motivational effect on managers.☞Weaknesses:⏹Require time, effort and money to prepare and keep updating. If managers spend toolong preparing/revising budgets, they will have less time to control and manage actual results⏹Managers may not see the value in the continuous updating of budgets⏹May be demotivating if targets are constantly changing⏹It may not be necessary to update budgets so regularly in a stable operatingenvironment.2.1.4Flexible budgets☞Recognizing the potential uncertainty, budgets designed to adjust costs levels according to changes in the actual levels of activity and output.☞Strengths:⏹Finding out well in advance the costs of idle time and so on if the output falls belowbudget.⏹Being able to plan for the alternative use of spare capacity if output falls short ofbudget☞Weaknesses:⏹As many errors in modern industry are fixed costs, the value of flexible budgets as aplanning tool are limited.⏹Where there is a high degree of stability, the administrative effort in flexiblebudgeting produces little extra benefit. Fixed budgets can be perfectly adequate in these circumstances.2.1.5Activity based budgeting☞Involves defining the activities that underlie the financial figures in each function and usingthe level of activity to decide how much resources should be allocated, how well it is being managed and to explain variance from budget.☞Strengths:⏹Ensures that the organisation’s overall strategy and any changes to that strategy willbe taken into account.⏹Identifies critical success factors which are activities that a business must perform wellif it is to succeed⏹Recognizes that activities drive costs; so encourages a focus on controlling andmanaging cost drivers rather than just the costs⏹Concentrate on the whole activities so that there is more likelihood of getting it rightfirst time.☞Weaknesses:⏹Requires time and effort to prepare so suited to a more complex organization withmultiple cost drivers.⏹May be difficult to identify clear individual responsibilities for activities⏹Only suitable for organization which have adopted an activity-based costing system⏹ABBs are not suitable for all organization, especially with significant proportions offixed overheads.2.1.6The future of budgeting☞Criticisms of traditional budgeting⏹Time consuming and costly⏹Major barrier to responsiveness, flexibility and change⏹Adds little value given the amount of management time required⏹Rarely strategically focused⏹Makes people feel undervalued⏹Reinforces department barriers rather than encouraging knowledge sharing⏹Based on unsupported assumptions and guesswork as opposed to sound,well-constructed performance data⏹Development and updated infrequently2.2Budgeting in not-for-profit organizations☞Special issues: the budget process inevitably has considerable influence on organizational processes, and represents the financial expression of policies resulting from politically motivated goals and objectives. The reality of life for many public sector managers is an subjected to(受---支配) growing competition.⏹Be prevented from borrowing funds⏹Prevent the transfer of funds from one budget head to another without compliancewith various rules and regulations⏹Plan one financial year.⏹Incremental budgeting and the bid system are widely used.2.3Evaluating the organisation’s move beyond budgeting2.3.1Conventional budgeting in a changing environment☞Weaknesses of traditional budgets:⏹Adds little value, requires far too much valuable management time⏹Too heavy a reliance on the ‘agreed’ budget has an adverse impact on managementbehavior, which can become dysfunctional(功能失调的) with regard to(关于) the objectives of the organization as a whole⏹The use of budgeting as a base for communicating corporate goals, is contrary to theoriginal purpose of budgeting as a financial control mechanism⏹Most budgets are not based on a rational, causal(因果关系的) model of resourceconsumption, but are often the result of protracted internal bargaining processes.⏹Conformance to budget is not seen as compatible with a drive towards continuousimprovement⏹Traditional budgeting processes have insufficient external focus.2.3.2The beyond budgeting model☞Rolling budgets focus management attention on current and likely future realities within the organizational context, it is seen as an attempt to keep ahead of change, or strictly speaking to be more in control of the response to the challenges facing the organization. ☞Benefits:⏹Creates and fosters a performance climate based on competitive success. Managerialfocus shifts from beating other managers for a slice(部分) of resources to beating the competition.⏹It motivates properly by giving them challenges, responsibilities and clear values asguidelines. Rewards are team-based⏹It empowers operational managers to act by removing resource constraints. Speedingup the response to environmental threats and enabling quick exploitation of new opportunities.⏹It devolves performance responsibilities to operational management who are closer tothe action.⏹It establishes customer-orientated teams that are accountable for profitable customeroutcomes.⏹Creates transparent and open information systems throughout the organization,provides fast, open and distributed information to facilitate control at all levels.3Business structure, IT development and other environmental and ethical issues3.1Business structure and information needs3.1.1Functional departmentation☞Information characteristics and needs: information flows vertically; functions tend to be isolated☞Implications for performance management⏹Structure is based on work specialism⏹Economies of scale⏹Does not reflect the actual business processes by which values is created⏹Hard to identify where profits and losses are made on individual products or inindividual markets⏹People do not have an understanding of how the whole business works⏹Problems of co-ordinating the work of different specialisms.3.1.2The divisional form☞Information characteristics and needs⏹Divisionalisation is the division of a business into autonomous regions⏹Communication between divisions and head office is restricted, formal and related toperformance standards⏹Headquarters management influence prices and therefore profitability when it setstransfer prices between divisions.⏹Divisionalisation is a function of organisation size, in numbers and in product-marketactivities.☞Implications for performance management⏹Divisional management should be free to use their authority to do what they think isright, but must be held accountable to head office⏹ A division must be large enough to support the quantity and quality of managementit needs⏹Each division must have a potential for growth in its own area of operations⏹There should be scope and challenge in the job for the management of the division☞Advantages:⏹Focuses the attention of subordinate(下级) management on business performanceand results⏹Management by objectives can be applied more easily⏹Gives more authority to junior managers, more senior positions⏹Tests junior managers in independent command early in their careers and at areasonably low level in the management hierarchy.⏹Provides an organisation structure which reduces the number of levels ofmanagement.☞Problems:⏹Partly insulated from shareholders and capital markets⏹The economic advantages it offers over independent organisations ‘reflectfundamental inefficiencies in capital markets’⏹The divisions are more bureaucratic than they would be as independent corporation⏹Headquarters management usurp divisional profits by management charges,cross-subsidies, unfair transfer pricing systems.⏹Sometime, it is impossible to identify completely independent products or markets⏹Divisionalisation is only possible at a fairly senior management level⏹Halfway house(中途地点)⏹Divisional performance is not directly assessed by the market⏹Conglomerate diversification3.1.3Network organisations☞Information characteristics and needs: achieve innovative response in a changingcircumstances; communication tends to be lateral(侧面的), information and advice are given rather than instructions(指令) and decisions.☞Virtual teams: share information and tasks; make joint decision; fulfil the collaborative function of a team)☞Implications for performance management⏹Staffing: shamrock organisation⏹Leasing of facilities such as IT, machinery and accommodation(住房)⏹Production itself might be outsourced⏹Interdependence of organisations☞Benefits: cost reduction; increased market penetration; experience curve effects.3.2Business process re-engineering3.2.1Business processes and the technological interdependence betweendepartments☞Pooled interdependence(联营式相互依赖): each department works independently to the others, subjects to achieve the overall goals☞Sequential interdependence(序列式相互依存): a sequence with a start and end point.Management effort is required to ensure than the transfer of resources between departments is smooth.☞Reciprocal interdependence(互惠式相互依存): a number of departments acquire inputs from and offer outputs to each other.3.2.2Key characteristics of organisations which have adopted BPR☞Work units change from functional departments to process teams, which replace the old functional structure☞Jobs change. Job enlargement and job enrichment☞People’s roles change. Make decisions relevant to the process☞Performance measures concentrate on results rather than activities.☞Organisation structures change from hierarchical to flat3.3Business integration3.3.1Mckinsey 7S model☞Hard elements of business behaviour⏹Structure: formal division of tasks; hierarchy of authority⏹Strategy: plans to outperform胜过its competitors.⏹Systems: technical systems of accounting, personnel, management information☞‘soft’ elements⏹Style: shared assumptions, ways of working, attitudes and beliefs⏹Shared values: guiding beliefs of people in the organisation as to why it exists⏹Staff: people⏹Skills: those things the organisation does well3.3.2Teamwork and empowerment☞Aspects of teams:⏹Work organisation: combine the skills of different individuals and avoid complexcommunication⏹Control: control the behaviour and performance of individuals, resolve conflict⏹Knowledge generation: generate ideas⏹Decision making: investigate new developments, evaluate new decisions☞Multi-disciplinary teams:⏹Increases workers‘ awareness of their overall objectives and targets⏹Aids co-ordination⏹Helps to generate solutions to problems, suggestions for improvements☞Changes to management accounting systems⏹Source of input information: sources of data, methods used to record data⏹Processing involved: cost/benefit calculation⏹Output required: level of detail and accuracy of output, timescales involved⏹Response required:⏹When the output is required:3.4Information needs of manufacturing and service businesses3.4.1Information needs of manufacturing businesses☞Cost behaviour:⏹Planning: standard costs, actual costs compared with⏹Decision making: estimates of future costs to assess the likely profitability of a product⏹Control: monitor total cost information☞Quality: the customer satisfaction is built into the manufacturing system and its outputs☞Time: production bottlenecks, delivery times, deadlines, machine speed☞Innovation: product development, speed to market, new process. Experience curve, economies of scale, technological improvements.☞Valuation:☞Strategic, tactical and operational information⏹Strategic: future demand estimates, new product development plans, competitoranalysis⏹Tactical: variance analysis, departmental accounts, inventory turnover⏹Operational: production reject rates, materials and labour used, inventory levels3.4.2Service businesses☞Characteristics distinguish from manufacturing:⏹Intangibility: no substance⏹Inseparability/simultaneity: created at the same time as they are consumed⏹Variability/heterogeneity异质性: problem of maintaining consistency in the standardof output⏹Perishability非持久性:⏹No transfer of ownership:☞Strategic, tactical and operational information⏹Strategic: forecast sales growth and market share, profitability, capital structure⏹Tactical: resource utilisation, customer satisfaction rating⏹Operational: staff timesheets, customer waiting time, individual customer feedback3.5Developing management accounting systems3.5.1Setting up a management accounting system☞The output required: identify the information needs of managers☞When the output is required:☞The sources of input information: the output required dictate the input made3.6Stakeholders’ goals and objectives3.6.1The stakeholder view☞Organisations are rarely controlled effectively by shareholders☞Large corporations can manipulate markets. Social responsibility☞Business receive a lot of government support☞Strategic decisions by businesses always have wider social consequences.3.6.2Stakeholder theory☞Strong stakeholder view: each stakeholder in the business has a legitimate claim on management attention. Management’s job is to balance stakeholder demands:⏹Managers who are accountable to everyone are accountable to none⏹Danger of the managers favour their own interests⏹Confuses a stakeholder’s interest in a firm with a person citizenship of a state⏹People have interest, but this does not give them rights.3.7Ethics and organisation3.7.1Short-term shareholder interest(laissez-faire自由主义stance)☞Accept a duty of obedience to the demands of the law, but would not undertake to comply with any less substantial rules of conduct.3.7.2Long-term shareholder interest (enlightened self-interest开明自利)☞The organisation’s corporate image may be enhanced by an assumption of wider responsibilities.☞The responsible exercise of corporate power may prevent a built-up of social and political pressure for legal regulation.3.7.3Multiple stakeholder obligations☞Accept the legitimacy of the expectations of stakeholders other than shareholders. It is important to take account of the views of stakeholders with interests relating to social and environmental matters.☞Shape of society: society is more important than financial and other stakeholder interests.3.7.4Ethical dilemmas☞Extortion: foreign officials have been known to threaten companies with the complete closure of their local operations unless suitable payments are made☞Bribery: payments for service to which a company is not legally entitled☞Grease money: cash payments to the right people to oil the machinery of bureaucracy.☞Gifts: are regard as an essential part of civilised negotiation.4Changing business environment and external factors4.1The changing business environment4.1.1The changing competitive environment☞Manufacturing organisations:⏹Before 1970s, domestic markets because of barriers of communication andgeographical distance, few efforts to maximise efficiency and improve management practices.⏹After 1970s, overseas competitors, global networks for acquiring raw materials anddistributing high-quality, low-priced goods.☞Service organisations:⏹Prior to the 1980s: service organisations were government-owned monopolies, wereprotected by a highly-regulated, non-competitive environment.⏹After 1980s: privatisation of government-owned monopolies and deregulation, intensecompetition, led to the requirement of cost management and management accounting information systems.☞Changing product life cycles: competitive environment, technological innovation, increasingly discriminating and sophisticated customer demands.☞Changing customer requirements: Cost efficiency, quality (TQM), time (speedier response to customer requests), innovation☞New management approaches: continuous improvement, employee empowerment; total value-chain analysis☞Advanced manufacturing technology(AMT): encompasses automatic production technology, computer-aided design and manufacturing, flexible manufacturing systems and a wide array of innovative computer equipment.4.1.2The limitation of traditional management accounting techniques in achanging environment☞Cost reporting: costs are generally on a functional basis, the things that businesses do are “process es’ that cut across functional boundaries☞Absorption costing(归纳成本计算法)☞Standard costing: ignores the impact of changing cost structures; doesn’t provide any incentive to try to reduce costs further, is inconsistent with the philosophy of continuous improvement.☞Short-term financial measures: narrowly focused☞Cost accounting methods: trace raw materials to various production stages via WIP. With JIT systems, near-zero inventories, very low batch sizes, cost accounting and recording systems are greatly simplified.☞Performance measures: product the wrong type of response☞Timing: cost of a product is substantially determined when it is being designed, however, management accountants continue to direct their efforts to the production stage.☞Controllability: only a small proportion of ‘direct costs’are genuinely controllable in the short term.☞Customers: many costs are driven by customers, but conventional cost accounting does not recognise this.☞The solution: changes are taking place in management accounting in order to meet the challenge of modern developments.4.2Risk and uncertainty4.2.1Types of risk and uncertainty☞Physical: earthquake, fire, blooding, and equipment breakdown. Climatic changes: global warming, drought;☞Economic: economic environment turn out to be wrong☞Business: lowering of entry barriers; changes in customer/supplier industries; new competitors and factors internal to the firm; management misunderstanding of core competences; volatile cash flows; uncertain returns☞Product life cycle:☞Political: nationalisation, sanctions, civil war, political instability☞Financial:4.2.2Accounting for risk☞Quantify the risk:⏹Rule of thumb methods: express a range of values from worst possible result to bestpossible result with a best estimate lying between these two extremes.⏹Basic probability theory: expresses the likelihood of a forecast result occurring⏹Dispersion or spread values with different possible outcomes: standard deviation.4.2.3Basic probability theory and expected valuesEV=ΣpxP=the probability of an outcome occurringX=the value(profit or loss) of that outcome4.2.4Risk preference☞Risk seeker: is a decision maker who is interested trying to secure the best outcomes no matter how small the chance they may occur☞Risk neutral: a decision maker is concerned with what will be the most likely outcome☞Risk averse: a decision maker acts on the assumption that the worst outcome might occur ☞Risk appetite is the amount of risk an organisation is willing to take on or is prepared to accept in pursuing its strategic objectives.4.2.5Decision rules☞Maximin decision rule: select the alternative that offers the least unattractive worst outcome. Maximise the minimum achievable profit.⏹Problems: risk-averse approach, lead to defensive and conservative, without takinginto account opportunities for maximising profits⏹Ignores the probability of each different outcome taking place☞Maximax: looking for the best outcome. Maximise the maximum achievable profit⏹It ignores probabilities;⏹It is over-optimistic☞Minimax regret rule: minimise the regret from making the wrong decision. Regret is the opportunity lost through making the wrong decision⏹Regret for any combination of action and circumstances=profit for best action in shoescircumstances – profit for the action actually chosen in those circumstances4.3Factors to consider when assessing performance4.3.1Political factors☞Government policy; government plans for divestment(剥夺)/rationalisation; quotas, tariffs, restricting investment or competition; regulate on new products.☞Government policy affecting competition: purchasing decisions; regulations and control;policies to prevent the concentration of too much market share in the hands of one or two producers4.3.2Economic environment☞Gross domestic product: grown or fallen? Affection on the demand of goods/services☞Local economic trends: businesses rationalising or expanding? Rents increasing/falling?The direction of house prices moving? Labour rates☞Inflation: too high to making a plan, uncertain of future financial returns; too low to depressing consumer demand; encouraging investment in domestic industries; high rate leading employees to demand higher money wages to compensate for a fall in the value of their wages☞Interest rates: affect consumer confidence and liquidity, demand; cost of borrowing increasing, reducing profitability;☞Exchange rates: impact on the cost of overseas imports; prices affect overseas customers ☞Government fiscal policy: increasing/decreasing demands; corporate tax policy affecting on the organisation; sales tax(VAT) affecting demand.☞Government spending:☞Business cycle: economic booming or in recession; counter-cyclical industry; the forecast state of the economic4.3.3Funding☞Reasons for being reluctant to obtain further debt finance:⏹Fear the company can’t service the debt, make the required capital and interestpayments on time⏹Can’t use the tax shield, to obtain any tax benefit from interest payments⏹Lacks the asset base to generate additional cash if needed or provide sufficientsecurity⏹Maintain access to the capital markets on good terms.4.3.4Socio-cultural factors☞Class: different social classes have different values。

资产重估中英文对照外文翻译文献

资产重估中英文对照外文翻译文献(文档含英文原文和中文翻译)资产重估研究摘要一般公认会计准则要求用不同方法来对资产的历史成本进行计价。

在这里，我们提供了一个简单的模型，而这种模型的变化，取决于管理目标和经济力量大小的不同。

该模型的主要特点是企业投资的资产依据的是无法沟通的私人信息。

当出现“柠檬问题”时，需要以强制审计的方式对其进行资产价值重估。

我们发现，最佳的升值策略可以通过看似繁多的资产重估方法来达到，这是一般公认会计准则的特点。

一、简介一般公认会计准则提供了一个令人眼花缭乱而又看似矛盾的的资产重估要求。

这些要求包括：成本或市价孰低法，可收回价值以净流量计价，无后续支出的固定资产采用成本与市价孰低计价，金融工具以公允价值计价。

我们研究了一个因现行规则影响的投资规模和资产价格重估模型。

我们发现，因规管目标和模型参数各异，上述政策都可以成为最佳的政策。

这一发现表明，标准的经济因素可能要求同时运用一般公认会计准则中规定的多项资产重估规则。

该模型的主要特色是一个简单的柠檬原理(乔治·阿克洛夫于1970年提出)，凡投资者收购一项资产，在转售开放市场之前，双方私下约定遵守“相关价值”的信息。

一些潜在的卖主们迫于清算其持有资产对资金流动性影响的担忧，同时，考虑到其他人可能通过私人信息了解因其流动性约束，进行模拟性投机。

正是这种模拟，形成了市场中的“柠檬问题”。

反过来，这种“柠檬问题”可能会影响预期的投资激励措施，作为企业家要预计“错误定价”，并认识到，如果他们最终成为流动性约束，他们可能无法赚取合理的投资回报。

反过来，强制重估实际上远离历史成本的低价值资产，可以在原则上形成更多的准确的价格，从而保护投资者的利益，提高投资回报。

然而，重估法规还可以要求对提出资产重估的一方承担这些昂贵的重估费用。

这些费用，反过来又可能扭曲投资决策，可能会影响的资产重估机构公正性。

对资产重估法规优化设计需要对这些收益和成本进行平衡考虑。

奖惩机制下的闭环供应链决策与协调研究

———————————————————————基金项目:宁夏自然基金项目，博弈理论在企业创新投入决策中的应用及优化研究（2023AAC03366）；宁夏高等学校科学研究项目，创新驱动发展下的企业投入决策及优化研究（NGY2022153）。

作者简介:黄彦丽（1980-），女，宁夏石嘴山人，本科，讲师，研究方向为应用数学。

0引言近年来，为缓解资源短缺，减轻环境承载压力，回收再制造逐渐成为发展循环经济、绿色经济的重要组成部分，越来越多的供应链企业开始实施闭环供应链运营管理，国内外学者也从不同的角度对闭环供应链进行了卓有成效的研究，如Ma 等[1]在考虑政府补贴策略下研究双渠道闭环供应链定价决策问题，黄彦丽等[2]从纵向持股的角度探讨了回收再制造供应链的决策与协调，研究表明投资持股有助于提高废旧产品回收率和实现供应链帕累托改进。

针对供应链“双重边际效应”问题，国内外学者以供应链系统利润最大化为原则设计协调契约，如成本分担契约、收益共享契约和两部定价契约等，有学者将讨价还价的思想引入供应链的协调当中，如陈金龙等[3]在信息不对称下，运用Rubinstein 轮流出价博弈思想研究了第三方金融服务商与银行、企业之间利率定价问题。

尽管讨价还价思想被广泛运用于实际问题的议价当中，但通过Rubinstein 轮流出价研究供应链协调问题的文献还相对较少。

基于此，本文在考虑奖惩机制下，针对单个制造商和单个零售商组成的回收再制造供应链决策与协调问题，分别构建分散决策和集中决策模型，并运用讨价还价的思想，设计Rubinstein 轮流出价协调策略，探析回收奖惩机制和贴现因子对供应链决策的影响，为供应链企业谈判和议价提供理论指导。

1问题描述与基本假设考虑由单个供应商和单个制造商组成的闭环供应链，供应商一方面用原材料生产零部件，另一方面通过设立回收站对废旧产品回收处理后作为原材料再利用。

下游制造商采购此零部件用于生产终端产品。

Optimization and Coordination of Fresh Product Supply Chains with Freshness-Keeping Effort

we study the following problem: A distributor procures a quantity of a fresh product from a producer and transports it to a target market for sale. ‘‘Obsolescence’’ and ‘‘deterioration’’ may occur during transportation, which cause ‘‘quantity loss’’ and ‘‘quality drop’’ (quality refers to the freshness of the product), respectively. The market demand for the product depends on the freshness of the product and the selling price. The distributor has to decide: (i) the quantity he should order from the producer, (ii) the freshnesskeeping effort he should invest during the transportation process, and (iii) the selling price in the market. The producer, on the other hand, has to determine the wholesale price. We consider decision making under both the decentralized and centralized settings and design an incentive scheme that coordinates the supplier–distributor channel.

Consumer environmental awareness and competition in two-stage supply

te change are increasingly considered as relevant as policy instruments to promote environmentally sound production practices (Anton et al., 2004; Delmas and Keller, 2005; Glachant, 2007; Dawson and Segerson, 2008). The ability to generate short-term economic gains must be present to promote acquiescence (Khanna, 2001), and the demand effects from product differentiation when consumers exhibit eco-friendly preferences (Ibanez and Grolleau, 2008; Conrad, 2005; Amacher et al., 2004).
Production, Manufacturing and Logistics
Consumer environmental awareness and competition in two-stage supply chains
Zugang (Leo) Liu a,1, Trisha D. Anderson b,⇑, Jose M. Cruz c,2
European Journal of Operational Research 218 (2012) 602–613
Contents lists available at SciVerse ScienceDirect

P2考官文章以及2011年删减的准则

Examiner’s reportP2 Corporate ReportingJune 2010General CommentsThe paper dealt with a wide range of issues and accounting standards. The paper was quite testing but candidates responded well resulting in a satisfactory pass rate. Candidates generally applied good examination techniques in answering the paper. However yet again there was evidence of candidates only answering two questions rather than the three questions required. This was particularly true of those candidates sitting the Malaysian and Hong Kong papers. Candidates seem to be answering the 50 mark question quite well but often the ethics section is not being answered. This would seem to suggest that either candidates have a problem with ethical issues which is a concern or candidates do not appreciate the importance of attempting all of the examination paper. An additional issue that was apparent was that candidates still do not have a good understanding of accounting for financial instruments which are examined frequently in this paper. An understanding of the accounting treatment of financial instruments is a fundamental pre-requisite for sitting this paper.Specific CommentsQuestion OneThe question required candidates to prepare a consolidated statement of comprehensive income, describe the amendments to the rules regarding reclassification of financial assets, and discuss how these rules could lead to ‘management of earnings’. Further candidates were asked to discuss the nature of and incentives for ‘management of earnings’ and whether such a process could be deemed to be ethically acceptable. Candidates generally performed well in this question. Candidates were required to calculate goodwill on the purchase of a subsidiary in order to determine the impairment of goodwill to be charged in the income statement. Candidates seemed to have a good knowledge of the calculation of goodwill under the full goodwill method. The question also dealt with the sale of an equity interest in a subsidiary which resulted in a positive movement in equity which was dealt by a movement on equity and not through other comprehensive income. Finally as regards the group accounting, candidates had to deal with the sale of a controlling interest which resulted in the retention of an associate interest. Generally candidates performed well this part of the question. The question also required candidates to deal with the accounting for an available-for-sale financial instrument using amortised cost. Candidates made a reasonable attempt atthis element of the question. Other elements of the question included dealing with revenue recognition, revaluation gains/losses on property, plant and equipment, calculating non controlling interest and accruing holiday pay for the entity. In a question such as this, it is very easy to make a mistake in calculation. Thus it is always important to show workings in a clear concise manner so that marks can be allocated for the principles and method used by the candidate.Part b of the question required knowledge of the recent change in accounting for the reclassification of financial instrument. Candidates did not perform well on this part of the question. It is important that candidates keep abreast of recent developments as the paper frequently examines recent pronouncements. Management of earnings was the topic which linked parts b and c. Candidates would benefit from wider reading in this area and also in the area of ethics. Often candidates’ answers are narrow and seem to lack application. A few hours researching management of earnings and ethics could be very beneficial. Candidates who answered part c on ethics performed satisfactorily.A good performance on question 1 by candidates is key to success in the paper. Good performance always s linked to answering all parts of the question and to a fundamental understanding of groupaccounting. However, candidates should not spend a disproportionate amount of time on the question.Question TwoThis question dealt with real world scenarios taken from corporate financial statements. It is important that the exam paper reflects actual issues in financial statements and that candidates can apply their knowledge to these scenarios. The first scenario dealt with deferred tax assets and their recognition in financial statements. This part of the question was well answered. Part b dealt with impairment of assets where an entity wished to use a Examiner’s report – P2 June 2010 1method not in accordance with the standard. It required candidates to apply their knowledge to the situation and not just repeat the rules in the standard. This part of the question was well answered. Part c looked at a situation where a company had a direct holding of shares and the subsidiary issued new shares which were not subscribed for by the holding company with the result that the interest was reduced to that of n associate. The question required candidates to determine whether the results should be presented based on principles provided by IFRS 5 Non-current Assets Held for Sale and Discontinued Operations. Candidates performed quite well on this part. The key to success is to set out the principles inthe standard and then to apply each one to the case in point.The final part dealt with the existence of a voluntary fund established in order to provide a post-retirement benefit plan to employees. The entity considered its contributions to the plan to be voluntary, and had not recorded any related liability in its consolidated financial statements. The entity had a history of paying benefits to its former employees, and there were several other pieces of information in the question. Candidates had to apply their knowledge of defined benefit schemes to the scenario. It did not require an in depth knowledge of the accounting standard but an ability to apply the principles. The question was answered satisfactorily by candidates.Question ThreeThis question was a case study type question based around a company in the edible oil industry. The company processed and sold edible oils and used several financial instruments to spread the risk of fluctuation in the price of the edible oils. Additionally, the company was unclear as to how the purchase of the brands and certain entities should be accounted for.It involved knowledge of derivatives, hedging and embedded derivatives at a fundamental level. Candidates did not have to apply their knowledge to any degree but simply had to recognisethe nature of the various financial instruments involved and discuss their accounting treatment. This knowledge is essential knowledge and will be examined in future diets. Candidates’ answers were satisfactory in the main but few candidates recognised the embedded derivative. The accounting for the brands was quite well answered with many students gaining high marks. The final part required candidates to apply IFRS 3 Business Combinations to a scenario. The answers were often quite poor with the main weakness being the application of the knowledge and the understanding of the nature of the purchase of the entities. Question FourThis question required candidates to discuss the reasons why the current lease accounting standards may fail to meet the needs of users and could be said to be conceptually flawed. The second part of the question required a discussion of a plant operating lease in the financial statements met the definition of an asset and liability as set out in the ‘Framework for the Preparation and Presentation of Financial Statements.’ Candidates’ answers were quite narrow in their discussion of the weaknesses in the accounting standards. The definitions of asset and liability were well rehearsed and candidates scored well on this part of the question. It is apparent that very few candidates read widely. This question always dealswith current issues which mean that a wider reading base is required to achieve a good mark. Accounting and Business, and the student accountant are just two examples of magazines that provide wider exposure to current issues.The final part of the question required candidates to show the accounting entries in the year of the sale and lease back assuming that an operating lease was recognised as an asset in the statement of financial position and to state how an inflation adjustment on a short term operating lease should be dealt with in the financial statements of an entity. The purpose of this question was to show how a change in the current accounting standards (by recognising operating leases in the statement of financial position) would affect their accounting treatment. The question was well answered and candidates scored well generally on this question. Examiner’s2011年P2考纲的变化ACCA发布了明年P2的考纲没有重大变化，还是原来8方面的能力，主要变化如下：1、新增-Accounting treatments applicable to SMEs-Requirements for a group to prepare consolidated financial statements, exemptions from preparation of financial statements and reasons directors may wish to exclude subsidiaries from consolidation-Entity reconstructions-Identify when an entity may no longer be a going concern-Circumstances where a reconstruction is an alternative to liquidation-Accounting treatment of reconstructions2、删除a) Evaluate the consistency and clarity of corporate reportsb) Assess the insight into financial and operational risks provided bycorporate reportsc) Discuss the usefulness of corporate reports in making investmentdecisionsd) Describe the principal objective of establishing a standard for enterprises reporting in the currency of a hyper-inflationary economye)Outline the issues in implementing a change to new accounting standards including organisational, behavioural, and procedural changes within the entityf) Apply and discuss the implications of a proposed change to an accounting standard on the performance and statement of financial position of an entityg) Discuss the implementation issues arising from the convergence processh)Identify the reasons for major differences in accounting practices, including culture3、以下准则不考了IAS 11Construction contractsIAS 29Financial reporting in hyperinflationary economiesIAS 41AgricultureSIC-12Consolidation – Special Purpose EntitiesSIC-13Jointly Controlled Entities –Non monetary Contributionsby VenturersSIC-15Operating Leases – IncentivesSIC-21Income Taxes – Recovery of Revalued Non-depreciable Assets SIC-27Evaluating the Substance of Transactions in the Legal Form of a LeaseSIC-32Intangible Assets – Website CostsIFRIC 1Changes in Existing Decommissioning, Restoration and Similar LiabilitiesIFRIC 4Determining Whether an Arrangement Contains a LeaseIFRIC 5Rights to Interests fromDecommissioning Restorationand Environmental Rehabilitation FundsIFRIC 7Applying the RestatementApproach under IAS 29,Financial Reporting in Hyperinflationary Economies IFRIC 9Reassessment of Embedded DerivativesIFRIC 10Interim Financial Reporting and ImpairmentIFRIC 12Service Concession ArrangementsIFRIC 13Customer Loyalty ProgrammesIFRIC 16Hedges of a Net Investment in a Foreign Operation IFRIC 17Distribution of non cash assets to owners12。

英文杂志

22
MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS
23
PDE, we were able to show that the option price is in fact a perturbation of the Black–Scholes price with an eﬀective constant volatility. Moreover, we derived a simple explicit expression for the ﬁrst correction in the singular perturbation expansion. We have shown that this correction is universal in this class of models and that it involves two eﬀective parameters which can easily be calibrated by using prices of liquid call options represented by the implied volatility surface. In this paper we introduce a class of multiscale stochastic volatility models. More precisely, we consider volatility processes which are driven by two diﬀusions, one ﬂuctuating on a fast time scale as in [5] and the other ﬂuctuating on a slow time scale, or, in other words, a slowly varying diﬀusion process. We show that it is possible to combine a singular perturbation expansion with respect to the fast scale with a regular perturbation expansion with respect to the slow scale. This again leads to a leading order term which is the Black–Scholes price with a constant eﬀective volatility. The ﬁrst correction is now made up of two parts which derive, respectively, from the fast and the slow factors and involves four parameters which still can be easily calibrated from the implied volatility surface. We show with options data that the addition of the slow factor to the model greatly improves the ﬁt to the longer maturities. The paper is organized as follows. In section 2 we introduce the class of stochastic volatility models that we consider and discuss the concepts of fast and slow time scales. This is done under the physical measure which describes the actual evolution of the asset price. In this section we also rewrite the model under the risk-neutral pricing measure which now involves two market prices of volatility risk. In section 2.4 we write down the pricing parabolic PDE which characterizes the option price P (t, x, y, z ) as a function of the present time t, the value x of the underlying asset, and the levels (y, z ) of the two volatility driving processes. For a European option the ﬁnal condition is of the form P (T, x, y, z ) = h(x). In section 3 we carry out the asymptotic analysis in the regime of fast and slow time scales. We use a combination of singular and regular perturbations to derive the leading order term and the ﬁrst corrections associated with the fast and slow factors. These corrections are nicely interpreted in terms of the Greeks (or sensitivities) of the leading order Black–Scholes price. The accuracy of this approximation is given in Theorem 3.6, the main result of this section. The proof is a generalization of the one presented in [8], where only the fast scale factor was considered. In section 4 we recall the concept of implied volatility and deduce its expansion in the regime of fast and slow volatility factors. This leads to a simple and accurate parametrization of the implied volatility surface. It involves four parameters which can be easily calibrated from the observed implied volatility surface. A main feature of our approach is that these calibrated parameters are explicitly related to the parameters needed in the price approximation formula and that, in fact, only these four parameters and the eﬀective constant volatility are needed rather than a fully speciﬁed stochastic volatility model. In section 5 we illustrate the quality of the ﬁt to the implied volatility surface by using options data. In particular we show that the introduction of the slow volatility factor is crucial for capturing the behavior of the surface for the longer maturities. In section 6 we show how to use our perturbation approach to price exotic options which are contracts depending on the path of the underlying process. 2. Multiscale stochastic volatility models. In this section we introduce the class of two-scale stochastic volatility models in which we consider and discuss the concept of a multiscale diﬀusion model. We also discuss the risk neutral or equivalent martingale measure that is used for pricing of options.

vauling mutual fund company

eScholarship provides open access, scholarly publishingservices to the University of California and delivers a dynamicresearch platform to scholars worldwide.Fisher Center for Real Estate and Urban Economics UC BerkeleyTitle:Valuing Mutual Fund CompaniesAuthor:Boudoukh, Jacob , IDC, NYU and NBER Richardson, Matthew , NYU and NBER Stanton, Richard , UC Berkeley Whitelaw, Robert F., NYU, Stern School of BusinessPublication Date:04-29-2004Series:Fisher Center Working PapersPublication Info:Fisher Center Working Papers, Fisher Center for Real Estate and Urban Economics, Institute of Business and Economic Research, UC BerkeleyPermalink:/uc/item/7ms3r416Keywords:Investment, Mutual Fund, Mortgage-Backed SecuritiesAbstract:Combining insights from the contingent claims and the asset-backed securities literatures, we study the economics of value creation in the asset management business. In particular, we provide a theoretical model and a closed form formula for the value of fund fees in the presence of the well known flow-performance relation, giving rise to interesting nonlinearities and volatility-related effects. The theoretical model sheds light on the role of fees, asset growth, asset and benchmark volatility, and the intensity of the flow-performance relation. To better understand the role of changing fund characteristics such as age and size on the fund value and fund risk, we estimate the empirical relation between returns and flows conditional on these characteristics for various asset classes. We study these effects using Monte Carlo simulations for various economically meaningful parameter values for specific asset classes. Measuring value as a fraction of assets under management, we find that both value and risk, systematic and idiosyncratic, decline in size and age. In addition, value is a complex, non-monotonic function of the fee charged on the fund.Valuing Mutual Fund Companies1Jacob Boudoukh a,Matthew Richardson b,Richard Stanton c and Robert F.Whitelaw bApril29,2004JEL classiﬁcation:G14.1a IDC,NYU and NBER;b NYU and NBER;c U.C.Berkeley.Contact:Prof.Robert Whitelaw,NYU, Stern School of Business,44W.4th St.,New York,NY10012,(212)998-0338,rwhitela@.We thank the Fisher Center for Real Estate and Urban Economics forﬁnancial support.Valuing Mutual Fund CompaniesABSTRACTCombining insights from the contingent claims and the asset-backed securities literatures,we study the economics of value creation in the asset management business.In particular,we provide a theoretical model and a closed form formula for the value of fund fees in the presence of the well knownﬂow-performance relation,giving rise to interesting nonlinearities and volatility-related eﬀects.The theoretical model sheds light on the role of fees,asset growth,asset and benchmark volatility,and the intensity of theﬂow-performance relation.To better understand the role of changing fund characteristics such as age and size on the fund value and fund risk,we estimate the empirical relation between returns andﬂows conditional on these characteristics for various asset classes.We study these eﬀects using Monte Carlo simulations for various economically meaningful parameter values for speciﬁc asset classes.Measuring value as a fraction of assets under manage-ment,weﬁnd that both value and risk,systematic and idiosyncratic,decline in size and age.In addition,value is a complex,non-monotonic function of the fee charged on the fund.1IntroductionAt the end of2002,the mutual fund industry managed over$11trillion dollars of assets worldwide according to data from the Investment Company Institute.Given the size of this industry,it is surprising that no literature has emerged which values mutual fund revenue streams.The literature to date has focused on documenting the performance of mutual funds,while a more recent literature links fundﬂows to this performance.1While there is considerable debate on the topic of whether mutual funds outperform relevant benchmarks, there is overwhelming evidence that fundﬂows depend on the ex post performance of mutual funds.This paper develops a valuation methodology for the feeﬂow generated by these mutual funds(“mutual fund valuation”henceforth).Speciﬁcally,we employ a contingent claims approach to mutual fund valuation by recognizing that mutual funds have the essential characteristics of asset-backed securities.The key insight underlying our valuation approach is that in an eﬃcient market the present value of a claim on the future value of an asset is simply a function of the current value of that asset.The result is that the value can be written in terms of three elements:(1)the current value of assets under management,(2) the volatility of assets under management(necessary for valuing option-like features induced by the link between fundﬂows and fund performance),and(3)a set of parameters that describe the fund(including the fees,the age,the size of assets,and parameters describing theﬂows into and out of the fund).Of particular interest,for the reasonable case where there is a positive link betweenﬂows and performance,the functional relation between the mutual fund value and the underlying net asset value of the fund is nonlinear.We are not theﬁrst to recognize that valuation in the asset management industry can be done using the contingent claims approach.Goetzmann,Ingersoll and Ross(2003)value hedge fund management businesses under incentive fees and high-water mark provisions. While their paper focuses on features that are speciﬁc to the hedge fund industry,one could infer mutual fund values that are similar to some special cases of the model provided below by assuming no incentive fees and no high-water marks.In addition,Boudoukh, McAllister,Richardson and Whitelaw(2000)value the revenue streams from deferred load (so-called B and C shares)mutual funds.Some of the insights from these papers carry through here.However,neither paper addresses a critical and complicating feature of mutual fund valuation,namely the evidence that theﬂow of capital into the fund(and thus the growth rate of the assets)depends on changes in the fund’s value and other characteristics 1See,for example,Elton,Gruber and Blake(1996),Gruber(1996),Carhart(1997),Chevalier and Ellison (1997)and Sirri and Tufano(1998),among others.of the fund.2This issue is key from a valuation perspective and highly relevant for the mutual fund industry,and is the focus of our paper.Methodologically,the closest analogy to our paper can be found in the mortgage-backed securities literature,and in particular empirical mortgage valuation models such as Schwartz and Torous(1989).That paper develops an approach for the valuation of a mortgage-backed security by incorporating an empirical model of mortgage prepayments into a simulation framework.Here,we develop a methodology for the valuation of mutual funds by building into our analysis an empirical model of fundﬂows.There are a number of similarities between the two approaches and the issues that arise.In the mortgage-backed case,prepayments depend on the underlying factor,i.e.,interest rates,as well as particular characteristics of the mortgages,such as age,burnout,and type.3In the mutual fund case,fundﬂows also depend on the underlying factor,i.e.,the change in the fund’s net asset value(e.g.,Chevalier and Ellison(1997)and Sirri and Tufano(1998)),as well as fund characteristics such as fund size(e.g.,Sirri and Tufano(1998)),age(e.g.,Chevalier and Ellison(1997)),and fund type (e.g.,Bergstresser and Poterba(2002)),among other variables.Moreover,the techniques for implementing the valuation frameworks are based on the same underlying methodology,i.e., Monte Carlo simulation(e.g.,Boyle(1977)).This paper provides several contributions to the currentﬁnance literature.First,we develop a methodology for understanding the value and risk of mutual fund revenue streams. In particular,we provide a closed-form solution for a model that incorporates fundﬂows as a function of relative performance.Though the underlying fundﬂow model is kept simple for analytical purposes,it identiﬁes some of the salient determinants of fund value.Mutual fund valuation depends both on the underlying asset value and its volatility,similar to asset-backed securities.Other determinants include asset growth and,in particular,the sensitivity of asset growth to relative performance.Interestingly,return volatility matters only to the extentﬂows correlate with net asset values.We also show that fees play an important role. On the one hand,higher fees increase current revenue,on the other hand,fees reduce growth. The combined eﬀect is ambiguous,depending on the parameters of the system.Second,using the existing empirical literature as an important guide,we build a more realistic empirical fundﬂow model and embed that model into a valuation framework for mutual funds.Though the empirical results provide some additionalﬁndings relative to2Goetzmann,Ingersoll and Ross(2003)do discuss this issue for hedge funds,but do not build this into the valuation framework per se.Moreover,they argue that the incentive fee structure limits the amount of assets going into the fund.3Schwartz and Torous(1989)assume mortgage termination is determined entirely by interest rate move-ments.More recent work includes additional factors such as house prices.See,for example,Kau,Keenan, Muller and Epperson(1992),and Downing,Stanton and Wallace(2003).the current literature,the most important contribution lies in being able to link identiﬁed fundﬂow determinants to mutual fund values.Most signiﬁcantly,our approach accounts for important state-and time-dependencies,such as how changes in funds’size and age aﬀect value.In particular,across all asset classes,we establish the importance of the eﬀects of age and size on assetﬂow properties such as growth,the sensitivity to performance,and volatility.Last,armed with economically meaningful parameters,we provide detailed comparative static analyses of fund value and risk characteristics for funds of diﬀerent asset classes for various fund sizes,ages,ﬂow volatilities and fees.Values throughout are measured in terms of the present value of fees per dollar of assets under management.We show how age,size and the fee level aﬀect fund value.In particular,older and/or larger funds are much less valuable,but are also less risky,when compared to young and/or small funds.This lower level of risk reﬂects both the volatility of the mutual fund value and its sensitivity to changes in the fund’s net asset value and benchmark return.In addition,we show that mutual fund values are a complex,non-monotonic function of the fee charged on the fund.The paper is organized as follows.Section2presents a closed-form solution(and cor-responding analysis)for valuing mutual funds when fundﬂows depend on changes in the underlying fund’s net asset value(NAV).In Section3,we present an empirical fundﬂow model for diﬀerent asset classes.In Section4,we describe the valuation approach under these more general assumptions about fundﬂow speciﬁcations.The valuation methodol-ogy is then implemented and analyzed for its implications for mutual fund values and risk measurement.Section5makes some concluding remarks and suggests directions for future research.2A Closed-form Solution to Mutual Fund ValuationWe develop our theoretical model in continuous time since this makes it easier to derive closed form pricing results in a contingent claims framework.Note that throughout this paper we assume that mutual funds have zero alphas,that is,fund managers do not possess superior skill at choosing undervalued assets.We make this assumption in order to avoid the debate about the presence of excess performance or lack thereof in the mutual fund industry. (See,for example,Ippolito(1992),Elton,Gruber and Blake(1996),and Carhart(1997)for diﬀering evidence,and Berk and Green(2002)for a recent theoretical paper addressing this issue.)As with the usual Black-Scholes framework,we assume that the net asset value of the fund,S t,follows a lognormal diﬀusion process.Ceteris paribus,the NAV of the fund will decline because of fees paid to the manager of the fund company as well as cash distributions(i.e.,dividends and capital gains)to investors.With respect to fees,we assume that the fee is paid continuously at(annualized)rate c.While in practice fees are generally taken out at discrete points,the fee as a constant proportion of assets is typical across all mutual funds. In this paper,we abstract from the issue of distributions.4The focus of this section is to characterize in a reasonable setting the relation between the fund’s value and the underlying assets under management whenﬂows depend on the fund’s performance.Under the risk-neutral measure,we can therefore write the NAV dynamics as:dS t=(r−c)S t dt+σS t dZ S,(1)where r is the risk-free rate,c is the management fee,σis the volatility and Z s is the Brownian motion associated with the underlying assets.In equation(1),mutual funds earn expected returns less than the underlying assets due to the fees paid to the mutual fund company.However,as long as the mutual fund cannot be shorted,there is no possibility of arbitrage.5Let the number of shares in the fund be N t,so that the total value of assets under management in the fund isV t=N t S t.The goal of our paper is to better understand the interaction between N and S in light of the existing empirical evidence and the eﬀect of this interaction on fund valuation.We treat the ﬂow of monies into and out of the fund as a lognormal diﬀusion process governed by,among other factors,a constant meanνand an independent volatility shockσN.As our empirical analysis shows there is an important fraction ofﬂow variations which is unexplained.As long as this variation is not correlated with the underlying NAV of the fund and can be diversiﬁed away within a broader set of asset holdings,this noise will have little impact on the fund’s value and priced risk(though not its idiosyncratic risk).However,the assumption that netﬂows depend on the change in the underlying NAV is clearly the most important piece of evidence and we incorporate this stylized fact below. In particular,we assume that theﬂow of monies into and out of the fund depends on the contemporaneous return of the NAV of the fund relative to some benchmark.We specify this dependence as a linear relation.Assume that the benchmark is given by index,I t,which4Note that most distributions are reinvested in the funds,so that the eﬀect on the underlying assets under management is small.That is,the NA V decline is oﬀset by the increase in the number of shares of the fund.5There does exist the important issue of why individuals invest in mutual funds in theﬁrst place under these circumstances.One possibility is that investors face lower transactions costs,either explicitly through trading constraints or implicitly through time constraints.Alternatively,mutual fund managers may possess superior investment skills,i.e.,positive alpha.follows a lognormal diﬀusion process.Under the risk-neutral measure,the dynamics of the index can be written as:dI t=rI t dt+σI I t dZ I,(2)dZ S dZ I=ρdt,(3)where Z I is the index’s Brownian motion,σI its volatility andρthe correlation between the fund’s NAV uncertainty and the index uncertainty.Assuming that the fundsﬂow in or out at a rate governed by a constantν,and that the netﬂows of the fund now depend linearly on its ex-post relative performance,we can write the netﬂows asdN t/N t=νdt+θ([dS t/S t−r]−γ[dI t/I t−r])+σN dZ N,(4)=(ν−θc)dt+θ(σdZ S−γσI dZ I)+σN dZ N.(5) dZ N dZ S=dZ N dZ I=0.(6)Several observations are in order.First,the parameterγdescribes the rule investors use to judge the fund’s performance versus the benchmark index.For example,γ=1compares the return on the fund’s NAV to the index’s return without adjusting for relative risk.A number of existing studies,such as Sirri and Tufano(1998),Chevalier and Ellison(1997)and Bergstresser and Poterba(2002),use this rule.Alternatively,lettingγequal the fund’s beta, i.e.cov(dS t/S t,dI t/I t)var(dI t/I t),we are assuming fund investors impose a one-factor model for describing excess performance.Gruber(1996),Del Guercio and Tkac(2002),and most performance measurement studies use this(and more elaborate)stly,γ=0is equivalent to investors looking at absolute rather than relative performance.Second,by linkingﬂows to net(and not gross)returns on the fund,there is a tendency for the netﬂows to decrease due to the negative eﬀect of fees on NAVs.Of course,in practice,these fees may be related to diﬀering alphas across funds.6As described earlier in this section,we are assuming that the managers of the funds do not have the ability to generate excess performance.In addition,there is considerable evidence linking bothνand θto the size of the fund,the type of fund,the fee structure,the fund’s age,etc.These features will be built into our empirical model of fundﬂows in the next section.Third,one of the main stylized facts from the empirical literature is that there is a lag between the realization of fund performance and its eﬀect on fundﬂows,one year being a typical lag chosen in this literature(e.g.,Sirri and Tufano(1998)).In the continuous-time 6However,the evidence in the literature tends to support the opposite conclusion(e.g.,Gruber(1996)).framework above(though not in later sections),we abstract from this feature and assume the eﬀect is instantaneous.This is not an important distinction for valuation.Since the fund’s value depends on the present value of all future fees,and these fees depend on the assets and netﬂows,whether theﬂow occurs this period or next period is a second-order eﬀect.Finally,putting aside the idiosyncratic risk,Z N,and index risk,Z I,the stochastic shocks to both NAV and netﬂows are drawn from the same source.This common shock induces a nonlinear relation between NAV and the value of the fund.This aspect of valuation is new to the literature on mutual funds.Deﬁne s t≡log S t,i t≡log I t,and n t≡log N t.By Ito’s Lemma,ds t=r−c−12σ2dt+σdZ S,(7)di t=r−12σ2Idt+σI dZ I,(8)dn t=ν−θc−12θ2σ2+γ2σ2I−2ρσγσI−12σ2Ndt+θ(σdZ S−γσI dZ I)+σN dZ N.(9)Integrating these equations,we obtainsτ=s t+r−c−12σ2(τ−t)+στtdZ S.(10)iτ=i t+r−12σ2I(τ−t)+σIτtdZ I.(11)nτ=n t+ν−θc−12θ2σ2+γ2σ2I−2ρσγσI−12σ2N(τ−t)+θστtdZ S+θγσIτtdZ I+σNτtdZ N.(12)From equations(10)–(12),sτ,iτand nτare normally distributed for allτ.Write M t,T for the present value of all fees between t and some terminal horizon,T(which might be inﬁnite).ThenM t,T=c E tTte−r(τ−t)Vτdτ,(13) or,switching the integral and the expectation,M t,T=cTt E te−r(τ−t)Vτdτ.(14)Since both n t and s t are normal,so is their sum,andE t e−r (τ−t )V τ =E t e n τ+s τ−r (τ−t ) ,=exp [E t (n τ+s τ)+1/2var t (n τ+s τ)−r (τ−t )].(15)From equations (10)and (12),we haveE t (s τ+n τ)=E t (s τ)+E t (n τ),=s t +n t + r +ν−c (1+θ)−12σ2−12θ2 σ2+γ2σ2I −2ρσγσI −12σ2N (τ−t ).(16)var t (s τ+n τ)=var t (s τ)+var t (n τ)+2cov t (n τ,s τ),=σ2(τ−t )+ θ2 σ2+γ2σ2I −2ρσγσI +σ2N (τ−t )+2 θσ2−θρσγσI (τ−t ).(17)Substituting into equation (15)and simplifying,we obtainE t e−r (τ−t )V τ =V t e −[c (1+θ)−ν−θσ(σ−ργσI )](τ−t ).(18)Finally,performing the integration in equation (14),we obtain 7M t,T =cV t T t e −[c (1+θ)−ν−θσ(σ−ργσI )](τ−t )dτ,=c 1−e −[c (1+θ)−ν−θσ(σ−ργσI )](T −t ) c (1+θ)−ν−θσ(σ−ργσI )V t .(19)Letting the terminal horizon go to inﬁnity,we haveM t ≡lim T →∞M t,T =c c (1+θ)−ν−θσ(σ−ργσI )V t for c (1+θ)>ν+θσ(σ−ργσI ).(20)Equations (19)and (20)provide the intuition for understanding the relation between mutual fund values and the value underlying assets under management.Unlike hedge funds,mutual funds tend not to disappear.This is partly due to the lack of a high watermark,but also to the fact that poorly performing funds are generally merged into existing funds so the assets do not disappear (Gruber (1996)).Therefore,since a long horizon setting may be 7As long as c (1+θ)=ν+θσ(σ−ργσI ).Otherwise,M t,T =c V t (T −t ).appropriate for analyzing the present value of fees,weﬁrst focus our intuition on the inﬁnite horizon case given by equation(20)and discuss theﬁnite horizon case in a later subsection. Theﬁnite horizon case is relevant,however,to the extent that we present evidence in the empirical section that the age of the fund has important implications for the parameters governing equation(20).These implications are equivalent to shortening the life of the fund.As aﬁrst pass at the intuition,consider the case in which fundﬂows are unrelated to fund performance,i.e.,θ=0.This is the typical environment that has been studied in the theoretical literature to date and therefore serves as a useful benchmark.Substitutingθ=0into equation(20),we getM t=cc−νV t for c>ν.(21)Equation(21)is essentially the Gordon growth model in which the initial cashﬂow is the fee earned on the assets under management,i.e.,cV t.Deﬁne the other parameters of the Gordon growth model as r∗for the discount rate and g for the growth rate.In the present case,g=r∗−c+ν.Since the assets are expected to grow at their expected return,adjusted for fees and exogenous growth,the expected return cancels.This is one of the central ideas of the paper,and for that matter any contingent claim analysis;that is,the present value of the future asset price is just today’s price.The present value of the fees then depends on the remaining two components of the growth rate.The fee,c,leads to a lower growth rate as the NAVs decline in c,whileνrepresents general growth in netﬂows not related to the NAV.Perhaps not surprisingly,this valuation formula suggests that the mutual fund business produces substantial revenue streams in a present value sense.8In particular,if we assume no growth in fundﬂows(i.e.,ν=0),then the fund’s value equals the current assets under management,V t.In other words,in present value terms,the management company extracts all the value of the assets.This is analogous to the house eventually owning the pot in a poker game by taking a small cut of each hand played.According to equation(21)the present value can even exceed current assets under management.It may,in fact,reach inﬁnity,for growth rates inﬂows that are larger than the management fee.The more interesting case,and the primary contribution of the paper,is to consider θ=0.As described in the introduction and above,this is the more empirically relevant case.The valuation formula in equation(20)now has two additional terms aﬀecting the growth rate of the cashﬂows.Theﬁrst term is cθ.Sinceθmeasures the sensitivity of the 8This equation is similar in spirit to the valuation of a hedge fund contract in Goetzmann,Ingersoll and Ross(2003)if one assumes no high water mark and no incentive fee.In their paper,they focus on hedge funds and treat the number of shares asﬁxed.They do assume,however,a constant withdrawal rate which is analogous to a negative value ofνin our case.netﬂows to the fund’s NAV return relative to the benchmark,and the fees cause the NAVs to drift downward through time,cθhurts the cashﬂow growth.The second term isθΣ, where we deﬁneΣ≡σ(σ−ργσI).Σhas a particularly interesting economic interpretation. It represents the covariance between the fund’s NAV return and the return relative to the benchmark,which determines netﬂows,namelyΣ=cov(dS t/S t,dS t/S t−γdI t/I t).That is,θΣis relevant for pricing to the extent that the return driving netﬂows is also correlated with the return on NAV.This is the convexity eﬀect that is common to option pricing and other asset-backed security pricing,such as mortgage-backed securities.2.1Comparative StaticsThe analysis above explains the primary components of the valuation of mutual fund revenue streams.How do these components aﬀect the valuation and under what conditions these components are important?Below,we provide some comparative statics analysis to help answer this question.2.1.1ΣAs long as the sensitivity of fundﬂow to performance is positive,i.e.,θ>0,then the value of the fund will be increasing in the covariance term,Σ.Note thatΣis increasing inσbut decreasing inρ,σI andγ.Hence,the value of the fund is increasing inσbut decreasing in ρ,σI andγ.This result relating value to the fund’sσhas also been documented by Goetzmann, Ingersoll and Ross(2003)but for completely diﬀerent reasons.Their result derives from the incentive fee in which hedge funds take a proportion of the return above the high-water mark. Here,even with no incentive fee,this result carries through because fundﬂow depends on the fund’s performance.Thus,many of the issues surrounding the incentives of fund managers discussed by Grinblatt and Titman(1989),Brown,Harlow and Starks(1996),Chevalier and Ellison(1997),Carpenter(2000),Das and Sundaram(2002)and Goetzmann,Ingersoll and Ross(2003)are relevant in our framework.Of some interest,Brown,Harlow and Starks(1996)and Chevalier and Ellison(1997) analyze the incentives of mutual fund managers to increase theﬂows into the fund.Under the assumption thatﬂows go more quickly into the very best performing funds(yielding an option-like payoﬀ),or under the assumption that investors look at year-end returns so that poor performers at mid-year have diﬀerent incentives,they argue and show empirically that managers may take more volatile positions.9In contrast,the result in equation(20) 9The empirical evidence in support of these claims is not universally accepted(e.g.,Busse(2001)).shows that neither the relative ranking nor nonlinearity in theﬂow-performance relation are important per se for the managerial incentive to take greater risk.This incentive arises quite naturally from the nonlinear payoﬀstructure.This is true even if theﬂow-performance relation is linear(as in equation(4)).The empirical results of Chevalier and Ellison(1997), as well some of the previously cited literature,are,however,important.Theyﬁnd thatθvaries across fund characteristics as well as across fund performance.The eﬀect of volatility on the mutual fund’s value depends very much on the sign and magnitude ofθ.A primary focus of our empirical analysis in Section3is,therefore,on characterizing the fund’sθas a function of the characteristics and performance of the fund.In contrast,as long asθ>0,the value of the fund will be decreasing in the volatility of the index and in its correlation with the fund’s NAV.Intuitively,the index serves as a counterweight to the fund’s own return volatility.Take the extreme case where the fund and index are perfectly correlated.Then the“volatility”eﬀect depends on the relative volatility of the fund versus the index,adjusted forγ.Thus,the incentives of managers described above relates to choosing assets which are both volatile and less correlated with the index subject to the constraints of a contract between investors and the fund(vis a vis the benchmark).Of some interest,this result does not depend on the“mutual fund tournament”explanation of Brown,Harlow and Starks(1996).Their eﬀect will just further accentuate our result here.One interesting example is that of index funds.To the extent index funds are perfectly correlated with the benchmark,and are risk-adjusted so thatγequals the fund’sβin a one-factor model,the value of the fund will be unrelated toΣ.Moreover,if this fund were holding some liquid assets,such as money-market accounts,and it was being judged as an index fund,then its value would actually decrease inΣ.In this example the concavity induced by the fund investor’s risk adjustment on the benchmark outweighs the convexity eﬀect induced by the fund’s own volatility.The example points out the relative importance of(i)the variance-covariance matrix between the fund and benchmark,and(ii)transparency between the fund and investors on what the appropriate benchmark should be.2.1.2cConsider how the fund’s value changes relative to the fees it charges.In the inﬁnite horizon case,weﬁnd a somewhat surprising result.Ifν+θΣ>0,then the mutual fund value actually falls as the manager increases the fee.The intuition is straightforward.Higher fees tend to decrease the net asset value of the fund over time.Sinceν+θΣ>0implies a positive growth rate inﬂows,the higher fee counteracts this positive growth.In a present value sense,it would be better to let theﬂows grow quickly and reap the present value of all future fees than take higher fees upfront.Note,however,that the present value of fees。

高级管理会计模拟试题（双语）

⾼级管理会计模拟试题（双语）ⅠPlease choose the best answers to the following questions. (20 points)1 A high-cost activity might prompt efforts to redesign or eliminate that activity entirely, a process called ( ).A continuous improvementB reengineeringC functional analysisD value engineering2 The costs associated with the resources acquired or contracted for in advance of when the actual work is done are ( ).A fixed cotsB fixed resourcesC committed costsD committed resources3 Which is the cost driver of batch-level activities ( )？A labor hoursB product specificationC material quantity processedD number of items in a purchase order4 Which is the best activity cost driver if the activity is supporting existing products ( )?A number of productsB number of production runsC number of setupsD number of machine hours5For a sales activity, such as support existing customers, we could use ( ) as a transaction driver.A cost per customer hourB actual cost per customerC cost per customerD number of machine hours6 What are the characteristics of low cost-to-serve customers? ( )A order custom productsB unpredictable order arrivalsC pay slowlyD electronic processing7 What are the big factors limiting the applicability of economists’pricing model? ( )A difficulty in estimating the demand curveB difficulty to use in realityC difficulty in estimating the cost curveD difficulty in identifying the cost drivers8 A supplier of telephone services charges a fixed line rental per period. The first 10 hours of telephone calls by the customer are free, after that all calls are charged at a constant rate per minute up to a maximum, thereafter all calls in the period are again free. Which of the following graphs depicts the total cost to the customer of the telephone services in a period? ( )9The total cost of production for two levels of activity is as follows:Level 1 Level 2Production（units）3,000 5,000Total cost （$）6,750 9,250The variable production cost per unit and the total fixed production cost both remain constant in the range of activity shown. What is the variable production cost per unit? ( )A $ 0.80B $ 1.25C $ 1.85D $ 2.2510 Which measures take the cost of capital into account? ( )A ROEB RIC ROID EV A11 A high-cost activity might prompt efforts to make the activity more efficient and less costly, a process called ( ).A continuous improvementB reengineeringC functional analysisD value engineering12 Resources acquired or contracted for in advance of when the actual work is done are ( ).A committed costsB committed resourcesC fixed cotsD fixed resources13 Which is the cost driver of unit-level activities ( )?A customer market supportB product specificationC labor hoursD number of items in a purchase order14 Which is the best activity cost driver if the activity is scheduling production jobs ( )?A number of machine hoursB number of production runsC number of setupsD number of products15 For a sales activity, such as support existing customers, we could use ( ) as a duration driver.A number of labor hoursB actual cost per customerC cost per customerD cost per customer hour16 What are the characteristics of high cost-to-serve customers? ( )A order standard productsB predictable order arrivalsC manual processingD electronic processing17 When total purchases of raw material exceed 30,000 units in any one period then all units purchased, including the initial 30,000, are invoiced at a lower cost per unit. Which of the following graphs is consistent with the behavior of the total materials cost in a period? ( )18 What are not the big factors limiting the applicability of economists’ pricing model? ( )A difficulty in calculating the cost driver rateB difficulty in estimating the demand curveC difficulty in estimating the cost curveD difficulty in identifying the cost drivers19An organization has the following total costs at three activity levels: Activity level (units) 8,000 12,000 15,000Total cost ($) 204,000 250,000 274,000Variable cost per unit is constant within this activity range and there is a step up of 10% in the total fixed costs when the activity level exceeds 11,000 units. What is the total cost at an activity level of 10,000 units? ( )A $ 234,000B $ 227,000C $ 224,000D $ 220,00020 The dysfunctional behavior from concentration on ROI was perceived probably under the influence of ( ) activities in 1980s.A GAAPB LBOC MBOD MVAⅡ Please fill the following blanks. (15 points)1When designing the optimal ABC system, one should balance the made from inaccurate estimates with the .2 The describes that the most profitable 20% of products generate about 300% of profits.3 Customers in the quadrant generate high margins and have low cost toserve.4 Recent work on (FMS) articulates how advanced manufacturing technologies can break through tradeoffs between mass production efficiency and flexibility.5 There are three broad phases in a product’s life cycle: , , .6 , , are some techniques of target costing.7 The role of is to direct the continuous improvement of process cost performance.8 EV A makes many adjustments such as , , to eliminate the distortions introduced by GAAP.9 is another costing tool to manage the total cost of quality. And is the variation of it.10 helps to derive a cost of capital based on the industry and risk characteristics of individual divisions.11 Economists show mathematically that firms in s somewhat monopolistic situation can maximize their profits at the price-output combination where equals .12 The capabilities of FMS and other information-intensive production technologies such as , , can all be viewed as greatly reducing the cost of performing batch and product-sustaining activities.ⅢPlease answer the following questions in your own words. (15 points)1 How many types of activity cost drivers are there in an ABC system? What is the difference between them?2 Please illustrate the types of quality costs with proper examples.ⅣRead the material and answer the following questions.Stellar Systems Company manufactures guidance systems for rockets used to launch commercial satellites. The company’s Software Division reported the following results for 20x1. Income…………………………………………………..$ 300,000Sales revenue………………………………………… … 2,000,000Invested capital (total assets)…………………………... 3,000,000Average balance in current liabilities…………………. 20,000Stellar Systems’weighted-average cost of capital (WACC) is 9 percent, and the company’s tax rate is 40 percent. Moreover, the company’s required rate of return on invested capital is 9 percent.Required：(1) Compute the Software Division’s sales margin, capital turnover,return on investment (ROI), residual income, and economic value added (EV A) for 20x1.(2) If income and sales remain the same in 20x2, but the division’s capital turnover improves to 80 percent, compute the following for 20x2: (a) invested capital and (b) ROI.。

cachon-Game theory in supply chain analysis

Game Theory in Supply Chain Analysis∗G´e rard P.Cachon†and Serguei Netessine‡The Wharton SchoolUniversity of PennsylvaniaPhiladelphia,PA19104-6366February2003AbstractGame theory has become an essential tool in the analysis of supply chains with multiple agents,often with conﬂicting objectives.This chapter surveys the applications of game theoryto supply chain analysis and outlines game-theoretic concepts that have potential for futureapplication.We discuss both non-cooperative and cooperative game theory in static anddynamic settings.Careful attention is given to techniques for demonstrating the existenceand uniqueness of equilibrium in non-cooperative games.A newsvendor game is employedthroughout to demonstrate the application of various tools.∗This is an invited chapter for the book“Supply Chain Analysis in the eBusiness Era”edited by David Simchi-Levi,S.David Wu and Zuo-Jun(Max)Shen,to be published by Kluwer.http://www.ise.uﬂ.edu/shen/handbook/†cachon@ and /˜cachon‡netessine@ and 1IntroductionGame theory(hereafter GT)is a powerful tool for analyzing situations in which the decisions of multiple agents aﬀect each agent’s payoﬀ.As such,GT deals with interactive optimization prob-lems.While many economists in the past few centuries have worked on what can be considered game-theoretic(hereafter G-T)models,John von Neumann and Oskar Morgenstern are formally credited as the fathers of modern game theory.Their classic book“Theory of Games and Economic Behavior”(von Neumann and Morgenstern1944)summarizes the basic concepts existing at that time.GT has since enjoyed an explosion of developments,including the concept of equilibrium (Nash1950),games with imperfect information(Kuhn1953),cooperative games(Aumann1959 and Shubik1962)and auctions(Vickrey1961),to name just a few.Citing Shubik(2002),“In the 50s...game theory was looked upon as a curiosum not to be taken seriously by any behavioral scientist.By the late1980s,game theory in the new industrial organization has taken over...game theory has proved its success in many disciplines.”This chapter has two goals.In our experience with G-T problems we have found that many of the useful theoretical tools are spread over dozens of papers and books,buried among other tools that are not as useful in supply chain management(hereafter SCM).Hence,ourﬁrst goal is to construct a brief tutorial through which SCM researchers can quickly locate G-T tools and apply G-T concepts.We hope this tutorial helps a SCM researcher quickly apply G-T concepts.Due to the need for short explanations,we omit all proofs,choosing to focus only on the intuition behind the results we discuss.Our second goal is to provide ample(but by no means exhaustive)references on the speciﬁc applications of various G-T techniques that could be utilized.These references oﬀer an in-depth understanding of an application where necessary.Finally,we intentionally do not explore the implications of G-T analysis on supply chain management,but rather,we emphasize the means of conducting the analysis too keep the exposition short.1.1Scope and relation to the literatureThere are many G-T concepts,but this chapter focuses on static non-cooperative,non-zero sum games,the concept which has received the most attention in the recent SCM literature.However, we also discuss cooperative games,dynamic(including diﬀerential)games,and games with asym-metric/incomplete information.We omit discussion of important G-T concepts that are covered in other chapters in this book:auctions are addressed in Chapters4and10;principal-agent models are covered in Chapter3;and bargaining is covered extensively in Chapter11.Certain types ofgames have not yet found application in SCM,so we avoid these as well(e.g.,zero-sum games and games in extensive form).The material in this chapter was collected predominantly from Moulin(1986),Friedman(1986), Fudenberg and Tirole(1991),Vives(1999)and Myerson(1997).Some previous surveys of G-T models in management science include Lucas’s(1971)survey of mathematical theory of games, Feichtinger and Jorgensen’s(1983)survey of diﬀerential games and Wang and Parlar’s(1989)survey of static models.A recent survey by Li and Whang(2001)focuses on application of G-T tools in ﬁve speciﬁc OR/MS models.1.2Game setupTo break the ground for our next section on non-cooperative games,we conclude this section by introducing basic GT notation.A warning to the reader:to achieve brevity,we intentionally sac-riﬁce some precision in our presentation.See texts like Friedman(1986)and Fudenberg and Tirole (1991)if more precision is required.Throughout this chapter we represent games in the normal form.A game in the normal form consists of(1)players(indexed by i=1,...,n),(2)strategies(or more generally a set of strategies denoted by x i,i=1,...,n)available to each player and(3)payoﬀs(πi(x1,x2,...,x n),i=1,...,n) received by each player.Each strategy is deﬁned on a set X i,x i∈X i,so we call the Cartesian prod-uct X1×X2×...×X n the strategy space(typically the strategy space is R n).Each player may have a unidimensional strategy or a multi-dimensional strategy.However,in simultaneous-move games each player’s set of feasible strategies is independent of the strategies chosen by the other players, i.e.,the strategy choice by one player is not allowed to limit the feasible strategies of another player.A player’s strategy can be thought of as the complete instruction for which actions to take in a game.For example,a player can give his or her strategy to a person that has absolutely no knowl-edge of the player’s payoﬀor preferences and that person should be able to use the instructions contained in the strategy to choose the actions the player desires.Because each player’s strategy is a complete guide to the actions that are to be taken,in the normal form the players choose their strategies simultaneously.Actions are adopted after strategies are chosen and those actions correspond to the chosen strategies.As an alternative to the“one-shot”selection of strategies in the normal form,a game can also berepresented in extensive form.Here players choose actions only as needed,i.e.,they do not make an a priori commitment to actions for any possible sample path.Extensive form games have not been studied in SCM,so we focus only on normal form games.The normal form can also be described as a static game,in contrast to the extensive form which is a dynamic game.If the strategy has no randomly determined choices,it is called a pure strategy;otherwise it is called a mixed strategy.There are situations in economics and marketing that have applied mixed strategies:e.g.,search models(Varian1980)and promotion models(Lal1990).However,mixed strategies have not been applied in SCM,in part because it is not clear how a manager would actu-ally implement a mixed strategy.(For example,it seems unreasonable to suggest that a manager should“ﬂip a coin”when choosing capacity.)Fortunately,mixed strategy equilibria do not exist in games with a unique pure strategy equilibrium.Hence,in those games attention can be restricted to pure strategies without loss of generality.Therefore,in the remainder of this chapter we consider only pure strategies.In a non-cooperative game the players are unable to make binding commitments regarding which strategy they will choose before they actually choose their strategies.In a cooperative game players are able to make these binding commitments.Hence,in a cooperative game players can make side-payments and form coalitions.We begin our analysis with non-cooperative static games.In all sections except the last one we work with the games of complete information,i.e.,the players’strategies and payoﬀs are common knowledge to all players.As a practical example throughout this chapter,we utilize the classic newsvendor problem trans-formed into a game.In the absence of competition each newsvendor buys Q units of a single product at the beginning of a single selling season.Demand during the season is a random variable D with distribution function F D and density function f D.Each unit is purchased for c and sold on the market for r>c.The newsvendor solves the following optimization problemmax Q π=maxQE D[r min(D,Q)−cQ],with the unique solutionQ∗=F−1Dµr−c r¶.(Goodwill penalty costs and salvage revenues can easily be incorporated into the analysis,but for our needs we normalized them out.)Now consider the G-T version of the newsvendor problem with two retailers competing on product availability.(See Parlar 1988for the ﬁrst analysis of this problem,which is also one of the ﬁrst articles modeling inventory management in a G-T framework).It is useful to consider only the two-player version of this game because only then are graphical analysis and interpretations feasi-ble.Denote the two players by subscripts i,j =1,2,i =j,their strategies (in this case stocking quantities)by Q i and their payo ﬀs by πi .We introduce interdependence of the players’payo ﬀs by assuming the two newsvendors sell the same product.As a result,if retailer i is out of stock,all unsatis ﬁed customers try to buy the product at retailer j instead .Hence,retailer i ’s total demand is D i +(D j −Q j )+:the sum of his own demand and the demand from customers not satis ﬁed by retailer j .Payo ﬀs to the two playersare then πi (Q i ,Q j )=E D h r i min ³D i +(D j −Q j )+,Q i ´−c i Q i i ,i,j =1,2.2Non-cooperative static gamesIn non-cooperative static games the players choose strategies simultaneously and are thereafter committed to their chosen strategies.Non-cooperative GT seeks a rational prediction of how the game will be played in practice.1The solution concept for these games was formally introduced by John Nash (1950)although some instances of using similar concepts date back a couple of centuries.The concept is best described through bestresponse functions .D efinition 1.Given the n −player game,player i ’s best response (function)to the strategies x −i of the other players is the strategy x ∗i that maximizes player i 0s payo ﬀπi (x i ,x −i ):x ∗i (x −i )=arg max x iπi (x i ,x −i ).If πi is quasi-concave in x i the best response is uniquely de ﬁned by the ﬁrst-order conditions.In the context of our competing newsvendors example,the best response functions can be found by optimizing each player”s payo ﬀfunctions w.r.t.the player’s own decision variable Q i while taking the competitor’s strategy Q j as given.The resulting best response functions are Q ∗(Q j )=F −1+r i −c i ,i,j =1,2.Some may argue that GT should be a tool for choosing how a manager should play a game,which may involve playing against rational or semi-rational players.In some sense there is no con ﬂict between these descriptive and normative roles for GT,but this philisophical issue surely requires more in-depth treatment than can be a ﬀorded here.Taken together,the two best response functions form a best response mapping R2→R2(or in the more general case R n→R n).Clearly,the best response is the best player i can hope for given the decisions of other players.Naturally,an outcome in which all players choose their best responses is a candidate for the non-cooperative solution.Such an outcome is called a Nash equilibrium (hereafter NE)of the game.D efinition2.An outcome(x∗1,x∗2,...,x∗n)is a Nash equilibrium of the game if x∗i is a best response to x∗−i for all i=1,2,...,n.Going back to competing newsvendors,NE is characterized by solving a system of best responses that translates into the system ofﬁrst-order conditions:Q∗1(Q∗2)=F−1D1+(D2−Q∗2)+µr1−c1r1¶,Q∗2(Q∗1)=F−1D2+(D1−Q∗1)+µr2−c2r2¶.When analyzing games with two players it is often instrumental to graph the best response functions to gain intuition.Best responses are typically deﬁned implicitly through theﬁrst-order conditions, which makes analysis diﬃcult.Nevertheless,we can gain intuition byﬁnding out how each player reacts to an increase in the stocking quantity by the other player(i.e.,∂Q∗i(Q j)/∂Q j)through employing implicit diﬀerentiation as follows:∂Q∗i(Q j)∂Q j =−∂2πii j∂πi2i=−r i f Di+(D j−Q j)+|D j>Q j(Q i)Pr(D j>Q j)r i f Di+(D j−Q j)+(Q i)<0.(1)The expression says that the slopes of the best response functions are negative,which implies an intuitive result that each player’s best response is monotonically decreasing in the other player’s strategy.Figure1presents this result for the symmetric newsvendor game.The equilibrium is located on the intersection of the best responses and we also see that the best responses are,indeed, decreasing.One way to think about a NE is as aﬁxed point of the best response mapping R n→R n.Indeed, according to the deﬁnition,NE must satisfy the system of equations∂πi/∂x i=0,all i.Recall that aﬁxed point x of mapping f(x),R n→R n is any x such that f(x)=x.Deﬁne f i(x1,...,x n)=∂πi/∂x i+x i.By the deﬁnition of aﬁxed point,f i(x∗1,...,x∗n)=x∗i=∂πi(x∗1,...,x∗n)/∂x i+x∗i→∂πi(x∗1,...,x∗n)/∂x i=0,all i.Hence,x ∗solves the ﬁrst-order conditions if and onlyif itis a ﬁxed point of mapping f (x )de ﬁned above.Figure 1.Best responses in the newsvendor game.The concept of NE is intuitively appealing.Indeed,it is a self-ful ﬁlling prophecy.To explain,suppose a player were to guess the strategies of the other players.A guess would be consistent with payo ﬀmaximization (and therefore reasonable)only if it presumes that strategies are chosen to maximize every player’s payo ﬀgiven the chosen strategies.In other words,with any set of strategies that is not a NE there exists at least one player that is choosing a non payo ﬀmaximizing strategy.Moreover,the NE has a self-enforcing property:no player wants to unilaterally deviate from it since such behavior would lead to lower payo ﬀs.Hence NE seems to be the necessary condition for the prediction of any rational behavior by players.While attractive,numerous criticisms of the NE concept exist.Two particularly vexing problems are the non-existence of equilibrium and the multiplicity of equilibria.Without the existence of an equilibrium,little can be said regarding the likely outcome of the game.If there are multiple equilibria,then it is not clear which one will be the outcome.Indeed,it is possible the outcome is not even an equilibrium because the players may choose strategies from di ﬀerent equilibria.In some situations it is possible to rationalize away some equilibria via a re ﬁnement of the NE concept:e.g.,trembling hand perfect equilibrium (Selten 1975),sequential equilibrium (Kreps and Wilson 1982)and proper equilibria (Myerson 1997).In fact,it may even be possible to use these re ﬁnements to the point that only a unique equilibrium remains.However,these re ﬁnements have generally not been applied or needed in the SCM literature.22These re ﬁnements eliminate equilibria that are based on incredible threats,i.e.,threats of future actions that would not actually be adopted if the sequence of event in the game led to a point in the game in which those actions could be taken.This issue has not appeared in the SCM literature.An interesting feature of the NE concept is that the system optimal solution(a solution that maximizes the total payoﬀto all players)need not be a NE.Hence,decentralized decision making generally introduces ineﬃciency in the supply chain.(There are,however,some exceptions:see Mahajan and van Ryzin1999b and Netessine and Zhang2003for situations in which competition may result in the system-optimal performance).In fact,a NE may not even be on the Pareto frontier:the set of strategies such that each player can be made better oﬀonly if some other player is made worse oﬀ.A set of strategies is Pareto optimal if they are on the Pareto frontier; otherwise a set of strategies is Pareto inferior.Hence,a NE can be Pareto inferior.The Prisoner’s Dilemma game is the classic example of this:only one pair of strategies is Pareto optimal(both “cooperate”),and the unique Nash equilibrium(both“defect”)is Pareto inferior.A large body of the SCM literature deals with ways to align the incentives of competitors to achieve optimality(see Cachon2002for a comprehensive survey and taxonomy).In the newsvendor game one could verify that the competitive solution is diﬀerent from the centralized solution as well,but this issue is not the focus of this chapter.2.1Existence of equilibriumA NE is a solution to a system of n equations(ﬁrst-order conditions),so an equilibrium may not exist.Non-existence of an equilibrium is potentially a conceptual problem since in this case it is not clear what the outcome of the game will be.However,in many games a NE does exist and there are some reasonably simple ways to show that at least one NE exists.As already mentioned,a NE is aﬁxed point of the best response mapping.Henceﬁxed point theorems can be used to estab-lish the existence of an equilibrium.There are three keyﬁxed point theorems,named after their creators:Brouwer,Kakutani and Tarski.(See Border1999for details and references.)However, direct application ofﬁxed point theorems is somewhat inconvenient and hence generally not done (see Lederer and Li1997and Majumder and Groenevelt2001a for existence proofs that are based on Brouwer’sﬁxed point theorem).Alternative methods,derived from theseﬁxed point theorems, have been developed.The simplest(and the most widely used)technique for demonstrating the existence of NE is through verifying concavity of the players’payoﬀs,which implies continuous best response functions.T heorem1(Debreu1952).Suppose that for each player the strategy space is compact and convex and the payoﬀfunction is continuous and quasi-concave with respect to each player’s own strategy. Then there exists at least one pure strategy NE in the game.If the game is symmetric (i.e.,if the players’strategies and payo ﬀs are identical),one would imagine that a symmetric solution should exist.This is indeed the case,as the next Theorem ascertains.T heorem 2.Suppose that a game is symmetric and for each player the strategy space is compact and convex and the payo ﬀfunction is continuous and quasi-concave with respect to each player’s own strategy.Then there exists at least one symmetric pure strategy NE in the game.To gain some intuition about why non-quasi-concave payo ﬀs may lead to non-existence of NE,suppose that in a two-player game,player 2has a bi-modal objective function with two local maxima.Furthermore,suppose that a small change in the strategy of player 1leads to a shift of the global maximum for player 2from one local maximum to another.To be more speci ﬁc,let ussay that at x 01the global maximum x ∗2(x 01)is on the left (Figure 2)and at x 001the global maximumx ∗2(x 002)is on the right (Figure 3).Hence,a small change in x 1from x 01to x 001induces a jump in the best response of player 2,x ∗2.The resulting best response mapping is presented in Figure 4and there is no NE in pure strategies in this game.As a more speci ﬁc example,see Netessine and Shumsky (2001)for an extension of the newsvendor game to the situation in which product inventory is sold at two di ﬀerent prices;such game may not have a NE since both players’objectives may be bimodal.Furthermore,Cachon and Harker (2002)demonstrate that pure strategy NE may not exist in two other important settings:two retailers competing with cost functions described by the Economic Order Quantity (EOQ)or two service providers competing with service times described by the M/M/1queuing model.(2π12Figure 2."(12x π12Figure 3.Figure 4.The assumption of a compact strategy space may seem restrictive.For example,in the newsvendorgame the strategy space R 2+is not bounded from above.However,we could easily bound it withsome large enough ﬁnite number to represent the upper bound on the demand distribution.That bound would not impact any of the choices,and therefore the transformed game behaves just as the original game with an unbounded strategy space.To continue with the newsvendor game analysis,it is easy to verify that the newsvendor’s objective function is concave(and hence quasi-concave)w.r.t.the stocking quantity by taking the second derivative.Hence the conditions of Theorem1are satisﬁed and a NE exists.There are virtually dozens of papers employing Theorem1(see,for example,Lippman and McCardle1997for the proof involving quasi-concavity,Mahajan and van Ryzin1999a and Netessine et al.2002for the proofs involving concavity).Clearly,quasi-concavity of each player’s objective function only implies uniqueness of the best response but does not imply a unique NE.One can easily envision a situation where unique best response functions cross more than once so that there are multiple equilibria(see Figure5).Figure5.Non-uniqueness of the equlibrium.If quasi-concavity of the players’payoﬀs cannot be veriﬁed,there is an alternative existence proof that relies on Tarski’s(1955)ﬁxed point theorem and involves the notion of supermodular games. The theory of supermodular games is a relatively recent development introduced and advanced by Topkis(1998).Roughly speaking,Tarski’sﬁxed point theorem only requires best response map-pings to be non-decreasing for the existence of equilibrium and does not require quasi-concavity of the players’payoﬀs(hence,it allows for jumps in best responses).While it may be hard to believe that non-decreasing best responses is the only requirement for the existence of a NE,consider once again the simplest form of a single-dimensional equilibrium as a solution to theﬁxed point mapping x=f(x)on the compact set.It is easy to verify after a few attempts that if f(x)is non-decreasing (but possibly with jumps up)then it is not possible to derive a situation without an equilibrium. However,when f(x)jumps down,non-existence is possible(see Figures6and7).Hence,increasing best response functions is the only(major)requirement for an equilibrium to exist;players’objectives do not have to be quasi-concave or even continuous.However,to describe an existence theorem with non-continuous payoﬀs requires the introduction of terms and deﬁnitions from lattice theory.As a result,we shall restrict ourselves to the assumption of continuous payoﬀfunctions,and in particular,to twice-diﬀerentiable payoﬀfunctions.Figure6.Increasing mapping.Figure7.Decreasing mapping.D efinition3.A twice continuously diﬀerentiable payoﬀfunctionπi(x1,...,x n)is supermodular (submodular)iﬀ∂2πi/∂x i∂x j≥0(≤0)for all x and all j=i.The game is called supermodular ifthe players’payoﬀs are supermodular.Supermodularity essentially means complementarity between any two strategies and is not linked directly to either convexity or concavity.However,similar to concavity/convexity,supermodular-ity/submodularity is preserved under maximization,limits and addition(and hence under expecta-tion/integration signs,an important feature in stochastic SCM models).While in most situations the sign of the second derivative can be used to verify supermodularity,sometimes it is necessary to utilize supermodularity-preserving transformations to show that payoﬀs are supermodular.Topkis (1998)provides a variety of ways to verify that the function is supermodular(some of his results are used in Netessine and Shumsky2001and Netessine and Rudi2003).The following theorem follows directly from Tarski’sﬁxed point result and provides another tool to show existence of NE in non-cooperative games:T heorem3.In a supermodular game there exists at least one NE.Coming back to the competitive newsvendors example,recall that the second-order cross-partial derivative was found to be∂2πi i j =−r i f Di+(D j−Q j)+|D j>Q j(Q i)Pr(D j>Q j)<0,so that the newsvendor game is submodular(and hence existence of equilibrium cannot be assured, recall Figure7).However,a standard trick is to re-deﬁne the ordering of the players’strategies. Let y=−Q j so that∂2πii =−r i f Di+(D j+y)+|D j>Q j(Q i)Pr(D j>−y)>0,so that the game becomes supermodular in(x i,y)and existence of NE is assured.Obviously,thistrick only works in two-player games(see also Lippman and McCardle1997for the analysis of themore general version of the newsvendor game using a similar transformation).Hence,we can statethat in general NE exists in games with decreasing best responses(submodular games)with twoplayers.This argument can be generalized slightly in two ways that we mention brieﬂy(see Vives1999for details).One way is to consider an n−player game where best responses are functionsof aggregate actions of all other players,that is,x∗i=x∗i³P j=i x j´.If best responses in such a game are decreasing,then NE exists.Another generalization is to consider the same game withx∗i=x∗i³P j=i x j´but require symmetry.In such a game,existence can be shown even with non-monotone best responses provided that there are only jumps up(but on intervals between jumps best responses can be increasing or decreasing).2.2Uniqueness of equilibriumFrom the perspective of generating qualitative insights,it is quite useful to have a game with a unique NE.If there is only one equilibrium,then you can characterize the actions in that equilibrium and claim with some conﬁdence that those actions should indeed be observed in practice.Unfortunately, demonstrating uniqueness is generally harder than demonstrating existence of equilibrium.This section provides several methods for proving uniqueness.No single method dominates;all may have to be tried toﬁnd the one that works.Furthermore,one should be careful to recognize that these methods assume existence,i.e.,existence of NE must be shown separately.2.2.1Method1.Algebraic argument.In some rather fortunate situations one can ascertain that the solution is unique by simply looking at the optimality conditions.For example,in a two-player game the optimality condition of one of the players may have a unique closed-form solution that does not depend on the other player’s strategy and,given the solution for one player,the optimality condition for the second player can be solved uniquely.See Hall and Porteus(2000)and Netessine and Rudi(2001)for examples. In other cases one can assure uniqueness by analyzing geometrical properties of the best response functions and arguing that they intersect only once.(Of course,this is only feasible in two-player games.See Parlar1988for a proof of uniqueness in the two-player newsvendor game and Majumder and Groenevelt2001b for a supply chain game with competition in reverse logistics.)However,in most situations these geometrical properties are also implied by the more formal arguments stated below.Finally,it may be possible to use a contradiction argument:assume that there is more than one equilibrium and prove that such an assumption leads to a contradiction,as in Lederer and Li(1997).2.2.2Method2.Contraction mapping argument.Although the most restrictive among all methods,the contraction mapping argument is the most widely known and is the most frequently used in the literature because it is the easiest to verify. The argument is based on showing that the best response mapping is a contraction,which then implies the mapping has a uniqueﬁxed point.To illustrate the concept of a contraction mapping, suppose we would like toﬁnd a solution to the followingﬁxed point equation:x=f(x),x∈R1.To do so,a sequence of values is generated by an iterative algorithm,{x(1),x(2),x(3),...}where x(1)is arbitrarily picked and x(t)=f³x(t−1)´.The hope is that this sequence converges to a uniqueﬁxed point.It does so if,roughly speaking,each step in the sequence moves closer to theﬁxed point. One could verify that if|f0(x)|<1in some vicinity of x∗then such an iterative algorithm converges to a unique x∗=f(x∗).Otherwise,the algorithm diverges.Graphically,the equilibrium point is located on the intersection of two functions:x and f(x).The iterative algorithm is presented in Figures8and9.Figure8.Convergingiterations.Figure9.Diverging iterations.The iterative scheme in Figure8is a contraction mapping:it approaches the equilibrium after every iteration.D efinition4.Mapping f(x),R n→R n is a contraction iﬀk f(x1)−f(x2)k≤αk x1−x2k,∀x1,x2,α<1.In words,the application of a contraction mapping to any two points strictly reduces(i.e.,α=1 does not work)the distance between these points.The norm in the deﬁnition can be any norm,。

Accounting Standards and Earnings Management Evidence from China

Accounting Standards and EarningsManagement:Evidence from China*DONGHUA ZHOU,Jiangxi University of Finance and EconomicsAHSAN HABIB,Auckland University of TechnologyABSTRACTThis article examines the eﬀect of an asset impairment–related regulatory reform on earnings management in China.Chinese Accounting Standard No.8(CAS No.8), which prohibits the reversal of long-lived asset impairments,was promulgated to constrain managerial opportunism with respect to previously recognized impairment loss reversal.CAS No.8forbids the reversal of long-lived asset impairment losses only,while allowing the reversal of short-term asset impairment losses.Based on a sample of China’s A-share listed companies on the Shanghai and Shenzhen Stock Exchange during the period2001–2008,we reveal that managers use less current asset write-downs and more reversals in the post–CAS No.8period.However,such reporting practices do not appear to be inﬂuenced by managerial incentives to avoid reporting losses and/or for“big bath”accounting purposes.Keywords Asset impairments;Earnings management;Long-lived assets;Short-term assetsNORMES COMPTABLES ET GESTION DU R ESULTAT:DONN EES CHINOISESR ESUM ELes auteurs e tudient l’incidence de la r e forme de la r e glementation chinoise relativea la d e pr e ciation des actifs sur la gestion du r e norme comptable n˚8 (CAS n˚8)de la Chine,qui interdit la reprise de d e pr e ciation des actifs a long terme,a e t e promulgu e e dans le but de restreindre le comportement opportunistedes dirigeants en ce qui a trait a la reprise de d e pr e ciation ant e rieurement con-stat e e.Cette norme proscrit la reprise de d e pr e ciation des actifs a long terme seule-ment,et non celle des actifs a court terme. A partir d’un e chantillon de soci e t e s chinoises dont les actions de cat e gorie A sont cot e es aux Bourses de Shanghai etde Shenzhen au cours de la p e riode2001–2008,les auteurs constatent que les diri-geants ont moins recours a la d e pr e ciation des actifs a court terme et davantage ala reprise de d e pr e ciation de ces actifs dans la p e riode post e rieure a l’adoption dela CAS n˚8.Ces pratiques ne semblent cependant pas^e tre inﬂuenc e es par la pro-pension des dirigeants a e viter la pr e sentation de pertes et(ou) a nettoyer le bilan. Mots clés:actifs a court terme,actifs a long terme,d e pr e ciation des actifs,ges-tion du r e sultat*We thank two anonymous reviewers and the editor for many constructive comments.AP Vol.12No.3—PC vol.12,n o3(2013)pages213–236©CAAA/ACPCdoi:10.1111/1911-3838.12016214ACCOUNTING PERSPECTIVES/PERSPECTIVES COMPTABLESThe purpose of this article is to examine the eﬀect on earnings management of a revised Chinese accounting standard relating to asset impairment:Accounting Stan-dard for Business Enterprises No.8—Impairment of Assets(hereafter CAS No.8). Although the literature on earnings management is voluminous,there is surprisingly scant empirical evidence on managerial use of speciﬁc accounting standards for earnings management purposes.We attempt toﬁll that void by documenting mana-gerial opportunistic use of asset impairment standards to manage earnings in China.China provides an interesting setting to examine the association between asset impairment and earnings management because of a regulatory change in the impairment standard.On February15,2006,the Chinese government announced that,beginning on January1,2007,all companies listed on the Chinese mainland stock exchanges will apply a set of38new accounting standards,referred to as the China Accounting Standards(CAS)system.CAS No.8prohibits listedﬁrms from reversing previous long-term asset impairment write-downs,although it continued to allow reversal of previously recognized short-term asset impairments.Regulators believed that such prohibition would reduce the extent to whichﬁrms use these write-downs to shift earnings between accounting periods and result in higher quality reported earnings(Zhang,Lu,and Ye,2010).This article empirically exam-ines whether such a regulatory initiative to makeﬁnancial statement information more informative has been successful in China.Prior empirical research has documented that managers strategically use impairment of assets to manage reported earnings(Jahmani,Dowling,and Torres, 2010;Riedl,2004;Zucca and Campbell,1992;Loh and Tan,2002).Jahmani et al. (2010)reveal that companies performing poorly are less likely to impair goodwill. Companies are also found to report more frequent asset impairment losses in years when earnings before asset impairment losses are lower than expected,giving rise to“big bath”accounting practices(Zucca and Campbell,1992).Riedl(2004)also documents a big bath accounting technique and also provides evidence of the rela-tionship between this reporting behavior and the reporting of asset impairment losses.Asset impairment losses are also reported in years when earnings before asset impairment losses are higher than expected,and this is done in order to achieve a smooth earnings pattern—a practice called income smoothing(Zucca and Campbell,1992).Elliott and Shaw(1988)show that management discretion will aﬀect the magnitude and timing of write-oﬀs related to reorganizations in a signiﬁcant and direct way,and asset impairment reversals provide management with a mechanism to smooth earnings.Zhang et al.(2010)examine the reaction to the promulgation of CAS No.8 that prohibits previously recognized impairment loss reversals and found that Chinese companies reported signiﬁcantly fewer asset impairment losses between the announcement date of CAS No.8to the eﬀective date(also called the transi-tion period)compared to those reported in the pre-announcement period.How-ever,companies with substantial levels of previously reported asset impairment losses reported more asset impairment reversals during this transition period than AP Vol.12No.3—PC vol.12,n o3(2013)ACCOUNTING STANDARDS AND EARNINGS MANAGEMENT IN CHINA215 in the pre-announcement period in order to reach certain earnings targets.These practices could be explained by the fact that managers were not allowed to reverse reported asset impairment losses partially in the year(s)after the transi-tion period.This article extends Zhang et al.(2010)by investigating not only long-term asset impairment reversals but also short-term asset impairment reversals as an instrument for earnings management.In order to provide more direct evidence about the eﬀect of CAS No.8on earnings management in China,this article examines asset impairments before and after CAS No.8implementation.Based on a sample of China’s A-share listed companies on the Shanghai and Shenz-hen Stock Exchange from the years2001and2008,the article reveals that man-agers use less current asset write-downs and more reversals in the post–CAS No.8period.However,such reporting practices do not appear to be inﬂuenced by managerial incentives to avoid reporting losses and/or for big bath account-ing purposes.This study contributes to the accounting literature in several ways.First,the ﬁndings enrich the sparse literature on earnings management through speciﬁc accruals,impairment of assets in this case.There is scant empirical evidence on the managerial response to the introduction of CAS No.8.To the best of our knowl-edge,no study has yet been done to examine the policy success of CAS No.8in the post-implementation regime.Second,theﬁndings shed light on the government regulatory eﬀorts to improve accounting standards in emerging markets.Regula-tors in China face the dilemma of whether they should allow moreﬂexibility in reporting standards so that managers can convey value-relevant private informa-tion,or limitﬂexibility in order to restrain management from making opportunistic accounting choices.The remainder of the article proceeds as follows.Section2reviews the related literature and develops testable hypotheses;section3explains the research design issues and is followed by an analysis of the main results in section4;and section5 concludes the article with a summary of theﬁndings and their implications for research and practice.LITERATURE REVIEW AND HYPOTHESIS DEVELOPMENTTo ensure thatﬁnancial statement users are not misled by poor qualityﬁnancial statements,organizations are required to prepareﬁnancial statements based on Generally Accepted Accounting Principles(hereafter GAAP).However,GAAP cannot be overly restrictive,and must allow forﬂexible reporting to permit manag-ers to convey their superior information about the operating environment of their businesses.This increases the value ofﬁnancial reporting as a relevant and credible form of communication.However,this same use of managerial judgment also creates opportunities for earnings management,where managers choose reporting methods and estimates with the intention of altering earningsﬁgures for theirAP Vol.12No.3—PC vol.12,n o3(2013)216ACCOUNTING PERSPECTIVES/PERSPECTIVES COMPTABLESpersonal beneﬁt(Healy and Wahlen,1999).Evidence from the academic literature has documented the pervasiveness of earnings management(e.g.,Burgstahler and Dichev,1997;Leuz,Nanda,and Wysocki,2003;Degeorge,Patel,and Zeckhauser, 1999)using aggregate accruals and the components of accruals as earnings management proxies.However,there has been relatively little research on the use of speciﬁc accruals or speciﬁc reporting standards as earnings management techniques.Strategic asset write-oﬀs and the subsequent reversal of write-oﬀlosses is one speciﬁc earnings management technique.1Frantz(1999)presents an analytical model demonstrating the existence of two equilibrium points for discretionary impairment of assets. First,management decides to report a restructuring provision where current earn-ings exceed the lower bound of the bonus plan and,second,management chooses to report a discretionary impairment of assets where a positive stock price eﬀect is expected.With an increase in asset write-downs over time,the literature started to inves-tigate the motivations for earnings management by strategic reporting of asset impairments.2Zucca and Campbell(1992)ﬁnd that the majority of their sample ﬁrms wrote down their assets in periods of below normal earnings(a“big bath”) and25percent of theﬁrms oﬀset the write-down with other gains or unusually high earnings(income smoothing).Francis,Hanna,and Vincent(1996)argue that economic factors and earnings management jointly determineﬁrms’asset write-down decisions.Francis et al.(1996)ﬁnd that write-oﬀs are more frequent and larger in magnitude if there has been a recent change in management and if the ﬁrm and/or its industry peer has taken write-oﬀs in the past.Riedl(2004)inter-prets some of his results as consistent with managers engaging in big bath report-ing behavior following the application of Statement of Financial Accounting Standards(SFAS)No.142.Strong and Meyer(1997)ﬁnd that the most important determinant of a write-down decision is a change in senior management and speculate that new manage-ment seeks to blame prior management for problems.Moehrle(2002)concludes thatﬁrms use restructuring charge reversals to beat analysts’forecasts and to avoid losses and declines in earnings.These prior research results support the contention that write-downs are used to manage earnings.In contrast,Rees,Gill,and Gore (1996)suggest the write-downs reﬂect economic considerations rather than oppor-tunistic behavior.Wilson(1996)concludes that the diverse results in this literature could be explained at least in part by measurement issues aﬀecting the write-down amount.1.Some exceptions include Moehrle(2002),Beaver,McNichols,and Nelson(2003),Altamuro,Beatty,and Weber(2005),and Frank and Rego(2006).2.For an early review of the asset write-down literature,see Alciatore,Dee,Easton,and Spear(1998).AP Vol.12No.3—PC vol.12,n o3(2013)ACCOUNTING STANDARDS AND EARNINGS MANAGEMENT IN CHINA217 China has witnessed remarkable economic growth over the last decade and, with it,has made signiﬁcant progress in the internationalization of its accounting standards,especially in the area of asset impairment.Beginning in1998,listed companies were required to recognize asset impairments for accounts receivable, inventories,and both short-and long-term investments.By2001,the recognition of asset impairments had been extended to cover four new categories of assets, includingﬁxed assets,construction in progress,intangible assets,and commission loans.Although this expansion in the coverage of assets to be impaired was intended to enhance the usefulness of accounting numbers by correcting overstated balance sheets,it also provided management with much more discretion in using asset impairment for managing earnings through the subsequent reversal of previ-ous write-downs(Chen,Wang,and Zhao,2009).Li(2001),for example,ﬁnds that companies tended to underestimate asset write-downs during the voluntary implementation period in1998.However,when write-downs became compulsory in1999,companies under(over)estimated asset impairments in order to report higher(lower)earnings.Chen et al.(2009)report that Chinese listed companies engage in earnings management through the reversal of asset impairment losses to reduce or avoid trading suspension or delisting.The authors also document that the value relevance of reversal information is nega-tively aﬀected by the earnings management motivated by regulatory incentives. Chen et al.(2009:593)conclude that“a seemingly improved accounting standard may not accomplish its intended objective of improvingﬁnancial reporting.”Simi-larly,Wang(2007)studied Chinese listedﬁrms’long-lived asset impairment write-down recognition and reversals during2001–2004,concluding that write-downs and their subsequent reversal result from earnings management incentives.Duh, Lee,and Lin(2009)ﬁnd that Taiwanese listedﬁrms recognizing more impairment losses are more likely to reverse impairment losses to avoid an earnings decline in a subsequent period.However,an eﬀective corporate governance mechanism con-strains such opportunistic reporting behavior.Chen,Chen,and Su(2004)suggest that the voluntary write-downs signal future performance improvement by docu-menting a positive valuation eﬀect forﬁrms that voluntarily wrote down their assets in1998in China.Prior research identiﬁes two strong incentives for managing earnings through asset impairment in China,namely,avoiding reporting losses and taking a big bath (Chen et al.,2004;Wang,2007;Zhang et al.,2010).If a public company reports losses for two consecutive years,it will carry a“special treatment”(ST)symbol. Companies with a ST symbol face some trading restrictions,including a daily price ﬂuctuation bracket of more than5percent,while the normal priceﬂuctuation allowed for a listed company is10percent.If the ST company continues to suﬀer a loss in the third year,it will be signiﬁed by a“*ST”and suspended from trading.A further loss in the following quarter will delist the company.Given such regula-tion,ﬁrms have a strong incentive to avoid reporting losses.Although public com-panies can use several speciﬁc accruals and accounting techniques to manage earnings,asset impairment is the most popular earnings management method inAP Vol.12No.3—PC vol.12,n o3(2013)218ACCOUNTING PERSPECTIVES/PERSPECTIVES COMPTABLESChina’s capital market.The reason is that asset impairments can be both write-downs(reducing proﬁt)and impairment loss reversals(increasing proﬁts),so they can be fully controlled by corporate managers.CAS No.8prohibits the reversal of asset impairments in order to restrict this earnings management behavior of Chinese managers.Zhang et al.(2010) analyze the policy eﬀect of current CAS in the transitional period andﬁnd that the introduction of CAS No.8only partially constrained managers’big bath behavior through strategic use of long-term asset impairment -pared with the old CAS regime(pre-2007),the current asset impairment stan-dards stipulate more clearly the recognition as well as the identiﬁcation criteria related to asset impairments.They not only require listed companies to make a judgment on indicators of asset impairments at the balance sheet date,but also stipulate in detail the indicators of asset impairments.Therefore,the current asset impairment standard contributes to standardizing the behavior of listed companies who used to arbitrarily or seldom write down assets,and also attempts to restrain public companies from reversing loss into proﬁt using asset impairments.On the other hand,the current asset impairments standard requires that the asset impairments cannot be reversed once recognized in an income statement, which may restrain companies motivated by the big bath incentive from recogniz-ing asset impairments in a loss year and reversing them in the following years.The old asset impairments standard was used as a tool of earnings management in public companies,which wrote down fewer asset impairments or reversed more asset impairments to avoid reporting losses.If they couldn’t avoid reporting losses, they would write down more asset impairments or reverse fewer asset impairments to take a big bath.CAS No.8prohibits the reversal of noncurrent asset write-downs but allows public companies to reverse current asset write-downs.Earnings management through current asset write-down and subsequent reversals may be an avenue for reaching earnings targets during the current CAS period.First,long-lived assets will be strictly regulated by government authorities and will require more careful audit evaluation.Because of the dominance of long-lived assets as a percentage of total assets,the recognition of impairment losses as well as rever-sals of previously recognized impairment losses will attract greater investor atten-tion and consequent market reaction.Second,according to CAS No.8,once asset impairment losses are recognized they cannot be reversed in a subsequent period.With the prohibition on impairment reversals,however,overstated asset impairments can no longer be used to shift earnings between accounting periods by reversing those impairment changes,and become less attractive to managers (Zhang et al.,2010).As a result,public companies may be more inclined to choose short-term asset impairments as an earnings management tool during the post–CAS No.8periods.This leads to the development of the following testable hypotheses:AP Vol.12No.3—PC vol.12,n o3(2013)ACCOUNTING STANDARDS AND EARNINGS MANAGEMENT IN CHINA219 H pared to the old accounting standards period,public companies are more likely to choose short-term asset impairments rather than long-lived asset impairments to avoid reporting losses.H pared to the old accounting standards period,public companies are more likely to choose short-term asset impairments rather than long-lived asset impairments for taking a big bath.RESEARCH DESIGNThe following model is used to test for the relation between asset impairment reversals as an earnings management tool to avoid reporting losses and to take a big bath.We are interested in whether or not the implementation of CAS No. 8can prohibit earnings management behavior in the Chinese capital market,and we added a dummy variable to measure the eﬀect of CAS No.8implementa-tion.We want to check the interactive eﬀect between these earnings management incentives and the implementation of CAS No.8.We estimate the following OLS regression:WD¼aþb0NASþb1LOSSþb2NASÃLOSSþb3BATHþb4NASÃBATHþb5SMOOTHþb6D INDROAþb7D ROAþb8MGTþb9ACCRþb10LEV þb11RETURNþb12SIZEþb13INSþb14ROE02þb15AUDITþeð1Þ: WD is(total impairment tÀtotal impairments tÀ1)/total assets tÀ1.Asset write-downs have positive values in computation of WD and reversals have neg-ative values;3NAS is a dummy variable coded one if the sample observations pertaining to 2007–2008(post–CAS No.8regime),or zero otherwise;LOSS is a dummy variable coded one if the company reported losses in the pre-ceding year but reports proﬁt in the current year(proxies for loss avoidance incentive),or zero otherwise;BATH equals net proﬁt before assets impairment reversals/opening assets,if LOSS is zero,and net proﬁt before assets impairment reversals/opening total assets<the median of its negative values,or zero otherwise;SMOOTH is a dummy variable coded one if LOSS is zero,and net proﬁt before assets impairment reversals>the median of its positive values,or zero otherwise;ΔINDROA is the change in the average growth in rate of return on assets(ROA) in industry(ROA is deﬁned as net income/total assets);ΔROA is change in ROA between year tÀ1and t;3.We thank an anonymous review for requiring clarity on the deﬁnition of WD.AP Vol.12No.3—PC vol.12,n o3(2013)220ACCOUNTING PERSPECTIVES/PERSPECTIVES COMPTABLESMGT is equal to one if LOSS equals zero and the incumbent president or general manager changed,or zero otherwise;ACCR is deﬁned as(ΔCAÀΔCLÀΔCASH+ΔSTDÀDEP+ΔTP),where ΔCA is change in current assets;ΔCL is change in current liabilities;ΔCASH is change in cash and cash equivalents;ΔSTD is change in current portion of the long-term debt;DEP is depreciation and amortization expenses;ΔTP is change in taxes payable.The total is deﬂated by lagged total assets to control for heteroskedasdicity;LEV isﬁrm leverage deﬁned as total liabilities/total assets;RETURN is market-adjusted returns for individual stocks for the period commencing in May and ending in April of the followingﬁscal year;SIZE is the natural logarithm of total assets;INS is a dummy variable coded one if the average returns of equity(ROE)in the past three years is between6and7percent,zero otherwise;ROE_02is a dummy variable coded one if the ROE is within[0–0.2percent]range (small proﬁt),or zero otherwise;AUDIT is a dummy variable coded one if the audit reports are unqualiﬁed,or zero otherwise.The coeﬃcient on NAS is expected to be negative following the argument that, because CAS No.8prohibits reversals of previously recognized long-lived asset impairment losses,managers will have less incentive in the post–CAS No.8period to recognize more long-lived asset write-downs.The interactive variable NAS*LOSS is hypothesized to be negative because CAS No.8will have a more pronounced adverse eﬀect onﬁrms trying to avoid reporting losses.The interactive variable NAS*BATH is also hypothesized to be negative because CAS No.8prohi-bition on the reversal of long-lived asset impairments will have a more pronounced adverse eﬀect onﬁrms trying to write down more asset impairments to take a big bath.A hypothetical illustration of diﬀerent types of earnings management incentives is provided in the appendix.The illustration identiﬁes cases where avoiding report-ing losses will be a stronger incentive than,say,income smoothing or big bath behavior.SAMPLE SELECTION,DESCRIPTIVE STATISTICS,AND EMPIRICAL RESULTS The sample includes all listedﬁrms in the Chinese A-share market during the period2001–2008.We retrieve information related to short-term and long-term asset impairments from the WIND database,andﬁnancial,market and manage-ment turnover data from the CSMAR database.Banks andﬁnancial institutions are excluded from the sample because of their distinct regulatory settings.Firm-AP Vol.12No.3—PC vol.12,n o3(2013)year observations are deleted if they lack suﬃcient ﬁnancial data to compute required ﬁnancial variables,or if they lack asset write-down information.We also delete ﬁrms which have been listed on the stock exchanges for less than three years,since we need to calculate ROE based on three successive years to ascertain ﬁrms’eligibility for seasoned equity oﬀerings (SEOs)in the capital market.These requirements result in a ﬁnal sample of 7,858ﬁrm-years with a total of 5,503(2,355)observations,coming from pre –CAS No.8(post –CAS No.8)periods respectively.We retain only those ﬁrms which have both pre –and post –CAS No.8observations available.Our ﬁnal sample consists of 1,396unique ﬁrms.Sample selection procedure is explained in Table 1.Panel A of Table 2provides descriptive statistics of the regression variables.The regression variables are winsorized at the top and bottom 1percent of their respective distributions to eliminate the inﬂuence of outliers.The average (median)write-down is À0.22percent (0.14percent)of the opening total assets.However,there is substantial variation among sample ﬁrms with respect to the variables of interest.The standard deviation of impairment write-downs is 0.25.Similar ﬁndings emerge for the components of WD (i.e.,long-and short-term asset impairment changes).Descriptive statistics on the three earnings management incentives,LOSS ,BATH ,and SMOOTH are presented next.The table shows that about 8percent of the sample observations,on average,tend to avoid reporting losses.The mean of BATH is À1percent,which is lower than that of LOSS .The mean and median of SMOOTH are 0.48and 0respectively.Sample observations experienced signiﬁcant management changes (an average of 41percent).Sample observations are leveraged,and larger in size.Mean (median)accruals are 20per-cent and 7percent of lagged total assets respectively.Mean and median industry-adjusted change in ROA is negative,suggesting a dismal ﬁnancial performance for the sample ﬁrms when benchmarked against industry averages.Average INS is 0.07suggesting that 7percent of the observations reported ROE between 6and 7TABLE 1Sample selection procedureObservationsInitial sample for the period 2001–200812,413Less:Observations pertaining to ﬁnancial institutions (238)Less:Firm-year observations without suﬃcientﬁnancial data including information on asset write-downs (1,017)Less:Firm-year observations listed on the stock exchange for less than 3years (3,300)Final sample7,858Pre-CAS 8observations 5,503Post-CAS 8observations 2,355Number of unique ﬁrms1,396ACCOUNTING STANDARDS AND EARNINGS MANAGEMENT IN CHINA 221AP Vol.12No.3—PC vol.12,n o 3(2013)T A B L E 2D e s c r i p t i v e s t a t i s t i c s a n d c o r r e l a t i o n a n a l y s i sP a n e l A :D e s c r i p t i v e s t a t i s t i c sV a r i a b l e s M e a n M e d i a nS D F i r s t Q u a r t i l e T h i r d Q u a r t i l eW D À0.00220.00140.25À0.00180.0069W D _S h o r t À0.00380.00260.370.00260.012W D _L o n g 0.000190.000.110.000.0009L O S S 0.080.000.280.000.00B A T H À0.0130.000.050.000.00S M O O T H 0.480.000.500.001.00ΔI N D R O A À0.35À1.222.07À2.23À0.43ΔR O A À0.33À0.157.24À0.660.24M G T 0.410.000.490.001.00A C C R 0.200.070.38À0.00450.18L E V 0.540.520.300.380.64R E T U R N 0.06À0.060.66À0.230.15S I Z E 21.3021.241.0320.6421.91I N S 0.070.000.260.000.00R O E _020.140.000.350.000.00A U D I T 0.901.000.301.001.00(T h e t a b l e i s c o n t i n u e d o n t h e n e x t p a g e .)222ACCOUNTING PERSPECTIVES /PERSPECTIVES COMPTABLESAP Vol.12No.3—PC vol.12,n o 3(2013)P a n e l B :D e s c r i p t i v e s t a t i s t i c s f o r t h e p r e –a n d p o s t –C A S N o .8p e r i o dV a r i a b l e s P r e –C A S N o .8p e r i o dP o s t –C A S N o .8p e r i o dM e a n M e d i a n S DF i r s t Q r t .T h i r d Q r t .M e a n M e d i a n S D F i r s t Q r t .T h i r d Q r t .W D 0.00180.00120.13À0.00230.0064À0.00410.00180.40À0.00070.0082W D _S h o r t À0.0010.00240.32À0.00280.011À0.0110.00300.48À0.00150.0136W D _L o n g 0.0020.000.07À0.0010.001À0.00400.000.17À0.00020.0004L O S S 0.0870.000.280.000.000.0740.000.260.00000.00B A T H À0.0170.000.080.000.00À0.0130.000.060.00000.00S M O O T H 0.490.000.460.001.000.470.000.510.001.00ΔI N D R O A À0.11À1.531.99À2.34À0.66À0.92À0.812.12À1.810.39ΔR O A À0.06À0.187.43À0.640.17À0.95À0.076.74À0.670.45M G T 0.430.000.490.001.000.380.000.480.001.00A C C R 0.050.050.13À0.010.120.540.680.530.031.03L E V 0.730.520.270.380.640.540.530.270.390.66R E T U R N À0.02À0.060.29À0.180.090.24À0.101.11À0.380.51(T h e t a b l e i s c o n t i n u e d o n t h e n e x t p a g e .)T A B L E 2(C o n t i n u e d )ACCOUNTING STANDARDS AND EARNINGS MANAGEMENT IN CHINA223AP Vol.12No.3—PC vol.12,n o 3(2013)。

a two_echelon inventory

A two-echelon inventory allocation and distribution center location analysisLinda K.Nozick *,Mark A.Turnquist 1School of Civil and Environmental Engineering,Cornell University,Hollister Hall,Ithaca,NY 14853-3501,USAReceived 6July 1999;received in revised form 14November 2000;accepted 26February 2001AbstractThe optimization of locations for distribution centers is in¯uenced by the demand for individual products.Lower demand products are often more e ectively held in more centralized locations than higher demand products.This paper presents a model for optimizing the location of inventory for individual products in a multi-product two-echelon inventory system and the integration of those decisions into the location analysis for distribution centers.A realistic application of the analysis process is dis-cussed.Ó2001Elsevier Science Ltd.All rights reserved.Keywords:Location analysis;Multi-echelon inventory;Logistics1.IntroductionTotal logistics costs (inventory plus transportation)in the US declined from about 13%of GDP in 1985,to about 10.5%in 1993,largely as a result of increasing emphasis on controlling in-ventories throughout the supply chain (Thomas,1997).However,since 1993,logistics costs (as a percentage of GDP)have been essentially constant.The ``easy''cost reductions have been made,and further improvements will require more e ective tools for an integrated analysis of inventory and transportation costs.One key question in designing a production±distribution system is locating distribution centers (DCs).There is a rich history of analytic work on facility location problems (see Dresner,1995),and one of the prime motivations for such analyses is locating distribution centers.However,itis Transportation Research Part E 37(2001)425±/locate/tre*Corresponding author.Tel.:+1-607-255-6496;fax:+1-607-255-9004.E-mail addresses:lkn3@ (L.K.Nozick),mat14@ (M.A.Turnquist).1Tel.:+1-607-255-4796;fax:+1-607-255-9004.1366-5545/01/$-see front matter Ó2001Elsevier Science Ltd.All rights reserved.PII:S1366-5545(01)00007-2426L.K.Nozick,M.A.Turnquist/Transportation Research Part E37(2001)425±441generally assumed that demands are known with certainty,and thus inventory costs are either neglected or assumed to be unrelated to the DC location decisions.Inventory costs(in particular,the safety stock required to provide a desired level of service when demand is uncertain)should be considered together with other facility operation and transportation costs in determining the optimal number of DCs and their locations.Recent work (Nozick and Turnquist,1998)has shown how to estimate a linear approximation for safety stock costs(for a set of products)as a function of the number of DCs.This allows the costs of safety stock to be included directly in a®xed-charge facility location model.Existing methods for solving the®xed-charge location problem can then be used to®nd the optimal number and locations for DCs with a more complete measure of total cost.Nozick and Turnquist apply this method to a single-echelon inventory±distribution system.This paper expands the analysis to consider a two-echelon system where decisions are made regarding what products to stock at each level,as well as where to locate the DCs.The number of DCs located and the demand for individual products at the DCs a ect which products they should stock.This in turn a ects the number of DCs that should be created. Hence,decisions regarding the number and location of distribution centers should be made jointly with decisions on stocking policies.This paper presents a method to determine which products should be held in inventory at both the DCs and a central location(e.g.,a plant or central warehouse),and which should be held only at the central location.The method is based on optimizing the trade-o between customer service and cost for each product.The inventory stocking policy is linked directly to a facility location model that determines the number and locations for DCs.Section2de®nes the distribution system considered in this paper.Section3describes the in-ventory model,and Section4treats the optimization of inventory across the two echelons.Section 5shows how this connects to a®xed-charge facility location model for the DCs.Section6contains an illustrative application of the model,and Section7provides conclusions and directions for further work.2.System de®nitionThe distribution system of interest in this paper includes one or more production plants,a set of distribution centers,retail outlets and customers.In this analysis,the number and location of the production plants is assumed®xed.The production plants(or a central warehouse also is assumed to be at a®xed location)are assumed to represent the®rst echelon of inventory.For the remainder of the paper,we will use the term``plant''to represent the central inventory location,although the analysis is also applicable if that location is really a warehouse.The number and locations of retail outlets that serve the customers are also assumed known.Assume that P di erent products,with uncertain demands,move through this distribution system and the demands for the various products are independent.That is,a temporary shortage of one product does not increase the demand for other products.The independence assumption allows the problem to be decomposed by product.Fig.1illustrates the¯ow of products from plants to retail outlets through DCs.Some products are held at the DCs in anticipation of customer demand at the retail outlets.Other products areheld at the plants only.Retail locations order replenishment stock from the DC to which they are assigned as products are demanded from them by their customers.The inventory policy adopted at the DCs is continuous review with one-for-one replacement.DCs backorder excess demand,and if a product normally stocked at the DC is out-of-stock,a penalty cost is incurred.Products that are stocked at the plants only are supplied to the DCs to ful®ll customer demands at the retail outlets only (i.e.,they ¯ow through the DCs to the retail outlets,but they are not stocked at the DCs).The inventory policy adopted at the plants is also continuous review with a one-for-one replacement.If a product is out of stock at the plant,the demand is backordered,and a penalty cost is incurred.The interrelated decisions on which we focus are:1.How many DCs should there be?2.Where should they be located?3.What products should be stocked at the DCs,and what products should be stocked only at the plant?The following two sections describe the inventory model and the formulation of the problem of determining what products should be stocked at each echelon.This inventory analysis is based on knowledge of the locations of DCs and the assignment of retail locations to DCs.Of course,these location and assignment decisions are made by the location analysis.The integration of the in-ventory and location analyses is the subject of Section 6.3.The inventory modelSuppose that there are N DCs,and that DC j (j 1;...;N )has n j retail locations assigned to it.Assume that retail location i (16i 6n j )has a Poisson demand for each product p in some set of products P ,with mean rate k ip .As a result,the demand for product p at DC j is a Poisson demand with a mean rateL.K.Nozick,M.A.Turnquist /Transportation Research Part E 37(2001)425±441427K jpX n ji 1k ip: 1The demand for product p at the plant(indicated by j 0)is also a Poisson demand process with a mean rateK0pX Nj 1K jp: 2If the demands for individual products,p,are independent,the inventory decisions are sepa-rable by product.The assumptions of Poisson demand and independence across products are consistent with assumptions found in the multi-echelon systems literature(e.g.,see Feeney and Sherbrooke,1966;Masters,1993;Forsberg,1995;Axs a ter and Zhang,1999).The following discussion of inventory levels and performance measures applies to each product separately,and the subscript p has been suppressed to simplify the notation.Assume the DC has an established inventory stock level of s j units,and orders one unit from the plant each time one is sent to a retail outlet.This one-for-one replacement policy has been suggested by several previous authors including Feeney and Sherbrooke(1966),Graves(1985), Masters(1993)and Forsberg(1995).If the plant has units of the product available in inventory,l1 is the mean delivery time from the plant to the DC once an order is placed.If the plant does not have any units of the product available,l2is the mean time required to resupply the inventory at the plant.An important level-of-service measure in inventory systems,where unsatis®ed customer de-mands are backordered,is the stockout rate,or the percentage of demand that cannot be satis®ed from on-hand inventory.In the presence of uncertain demand,an amount of safety stock will be carried to reduce the stockout rate.Safety stocks for various products in a multi-echelon distribution system may be determined (see Masters,1993)using a model for inventory based on Palm's Theorem(see Feeney and Sherbrooke,1966).The essential idea underlying this model is that if demand is Poisson dis-tributed and replacements are made on a one-for-one basis,the total number of units in re-plenishment(on order)is also Poisson distributed.If the demand rate at the DC is K j,and the average replenishment time is l1,then the number of units on order,m j,is Poisson distributed with parameter K j l1.If the established stock level is s j,then the probability of a stockout is simply Pr m j>s jPr m j>s jX Ik s j 1eÀK j l1 K j l1 kk!: 3At the plant(or central inventory location),the arrival rate is K0,the mean replenishment time is l2,and the stock level is s0.The corresponding version of(3)for the stockout probability at the plant isPr m0>s0X Ik s0 1eÀK0l2 K0l2 kk!: 4428L.K.Nozick,M.A.Turnquist/Transportation Research Part E37(2001)425±441Backorders at the plant do not necessarily reduce the service level at the DCs.As long as stock remains at the DCs,the stockout at the plant is not noticed.However,if backorders accumulate at the plant,it becomes more likely that the DCs will be a ected because the replenishment time at the DCs becomes longer.The average additional waiting time at the DCs is the expected number of backorders at the plant,divided by the demand rate,K0(Masters,1993)W0X Ik s0 1 k(Às0 eÀK0l2 K0l2 kk!),K0: 5This computation of W0represents an application of Little's law(Little,1961).The expected replenishment time from the plant to the DCs is thenl H1 l1 W0 6 and l H1should be used in(3),rather than l1.This violates the assumption that the demand and resupply processes are independent,but the di culties are likely to be minor(see Masters,1993; Diks et al.,1996).Related treatments of multi-echelon systems are contained in Sherbrooke (1968),Simon(1971)and Graves(1985).If a maximum allowable stockout probability is speci®ed,the minimum required stock level,sÃj, can be found for a DC,using(3),and sÃ0can be found for the plant using(4).The stock levels found will include both cycle stock and safety stock.The cycle stock at DC j is K j l H1and the safety stock is sÃjÀK j l H1.At the plant,the cycle stock is K0l2and the safety stock is sÃ0ÀK0l2.The following discussion is primarily concerned with the size of the safety stock,since safety stock is the portion of total stock that is sensitive to the number and location of DCs.4.Optimizing inventory location and quantitySo far,we have illustrated how to®nd the minimum inventory necessary for given stockout rate at the DCs sÃj and the plant sÃ0 .One approach to optimizing inventory policies is to minimize the sum of the costs resulting from stockouts and inventory holding costs.Masters(1993)for-mulates such a model,based on an assumption that stockouts at retail outlets result in lost sales, and stockouts further up the distribution chain are backordered.His formulation minimizes the expected cost of lost sales plus inventory holding costs.We have taken a similar approach,but our approach minimizes the expected penalties for stockouts at the DCs and the plant,along with inventory holding costs.Denote the probability of a stockout at DC j(as a function of the inventory stock level)by r j s j ,and the corresponding probability at the plant by r0 s0 ,as de®ned by(3)and(4),respectively.In the distribution system under analysis here,there are two types of stockout situations.The stockout may occur at the DC only,or at both the DC and the plant simultaneously.The second situation is clearly more onerous than the®rst.Suppose the penalty cost of a stockout at the DC when the order can be ®lled from the plant's inventory is a,and the penalty cost of simultaneous stockouts at the DC and the plant is b b>a .Suppose also that these penalties can be expressed as equivalent dollars, so they can be compared directly to the annual holding cost,h,for a unit of inventory.L.K.Nozick,M.A.Turnquist/Transportation Research Part E37(2001)425±441429For Poisson demands,the ``Poisson arrivals see time averages''(PASTA)property (Wol ,1982)implies that the expected number of stockouts over an annual period is the product of the arrival rate and the stockout probability.This lets us formulate the following model:min s 0;s 1;...;s N a 1Àr 0 s 0 X N j 1K j r j s j b r 0 s 0 X N j 1K j r j s j h X N j 0s j : 7 Eq.(7)is a nonlinear optimization whose only constraints are nonnegativity restrictions on s 0;s 1;...;s N .Local minima of Eq.(7)can be found quite e ciently using any of several available commercial software packages.However,Eq.(7)is not a convex function of the decision vari-ables,so some additional care must be taken to assure that a local minimum found is also a global minimum.The expression to be minimized in Eq.(7)shows how the inventory policy (setting values for s 0;s 1;...;s N )depends on the number of DCs (N)and on their locations (which de-termine the assignments of customers,and hence the values for K j ;j 1;...;N ).The solution to Eq.(7)also implies optimal stockout probabilities at the DCs and at the plant,through r j s j and r 0 s 0 ,respectively.In order to focus on the inventory allocation implications of (7)for a moment (apart from the DC location e ects),consider a hypothetical situation in which we have N 20DCs,and the total demand is equally divided among them.Suppose that the average annual holding cost h is $4000(which might be typical of vehicles held in inventory by an automotive manufacturer,for example).Suppose that the penalties associated with stockouts are a $100and b $500.Further,assume that l 1 7days and l 2 21days.Fig.2illustrates the optimal composition of the stock as a function of annual demand for this sample set of problem parameters.When demand is very small (<500units per year,or <25units per year for each DC)it is not economical to hold safety stock at either the DCs or the plant.For very low demand items (at least for the parameter values used in this example),it is more economical to operate in a ``build to order''mode,accepting the stockout penalties in order to minimize the holding costs.For relatively low demand items (approximately 500±4000units per year,or about 25±200units per DC per year),most safety stock is held at the plant.As demand rises,the required safety stock (as a proportion of total stock)falls,and most of that safety stock shifts to the DCs.Fig.3illustrates the optimal stockout rates at the DCs and plants as functions of total annual demand.For very low volume products it is desirable not to hold safety stock at either theplants430L.K.Nozick,M.A.Turnquist /Transportation Research Part E 37(2001)425±441or the DCs.Therefore,the stockout rates are high in both locations.For products whose annual volumes are in the range of 500±4000units,the safety stock is held centrally,and the plant stockout probability falls rapidly.The optimal level of stockouts at the DCs is quite high,but the safety stock at the plant ensures a reasonable level of service.As volume increases to above 4000units per year,there is incentive to protect against stockouts at the DCs,and the increasing level of safety stock at the DCs creates a declining stockout probability there.In general,as the demand rate rises,and the optimal solution is to put enough stock into the DCs to reduce the overall stockout probability,there is reduced need for safety stock at the plant,and the allowable stockout rate there increases.The behavior of the optimal solution suggests that it may be appropriate from a managerial perspective to divide products into two groups,those to be held only at the plant and those that will be stocked at both the DCs and the plant.We can then de®ne a service level (stockout probability)for each group.For example,a possible decision rule might be to only hold inventory at the DCs for products that have an annual demand su cient to warrant a stockout rate of no more than 10%at the DCs.In this example and under this rule,the DCs would stock all products with an annual demand of more than 10,000units (see Fig.3),or 500units per DC.This underscores the fact that there is an interaction between the number of DCs and the products to be held at each of the DCs.In general,as more DCs are used,there will be fewer products stocked at the DC level of the distribution system because there will be fewer products whose total annual demand per DC meets the threshold criterion.If DCs vary widely in level of demand served,some products may be held at some DCs and not at others.The speci®c level of demand that acts as a threshold in this example is obviously dependent on the parameters assumed,but the model speci®ed in Eq.(7)allows con-struction of policies for the parameters appropriate to any speci®c situation.5.Optimizing the number and location of distribution centersIn Section 3,we developed a method for specifying the minimum inventory level necessary to ensure a speci®ed stockout probability for a given product.In Section 4we combined thismethod L.K.Nozick,M.A.Turnquist /Transportation Research Part E 37(2001)425±441431with cost parameters related to stockouts and holding costs to create a model that can be solved to determine optimal stock levels at each echelon for a given product.Throughout Sections3and4, we have decomposed the analysis by product,and suppressed the product p subscript on variables to simplify the notation.For each product,the optimal inventory policy is dependent on the number of DCs operated(N),and on the locations of those DCs(which determines the demands, K jp,for j 1;...;N,served by each DC).Previous work by Nozick and Turnquist(1998)has shown how incorporating inventory costs in a location model can a ect optimal decisions on the number and locations of DCs.The focus in this section is on constructing an iterative procedure that can alternate between solving a location problem(given an inventory policy),and solving an inventory optimization(given the number an locations of DCs).In this way,a method can be created for integrating the inventory and location decisions.The basis for representing inventory costs in the location decisions found in Nozick and Turnquist(1998)is that for a speci®ed stockout rate and total demand for a given product,p,the total safety stock for that product that must be held across all the DCs can be accurately ap-proximated as a linear function of the number of DCs(N).This allows the safety stock inventory costs to be included in the®xed-charge coe cient on potential sites in a®xed-charge location model.In this way,the inventory costs have a direct in¯uence on the number of DCs sited and their locations.The current analysis follows a similar path,but the cost coe cient used in the location model to re¯ect the cost of safety stock inventory must represent the solution to the model in Eq.(7),at least in an approximate way.Then,given this cost coe cient as a®xed-charge for locating a DC,the location model is solved for the number and locations of DCs to be operated,as well as the demand to be served by each DC.This solution is used to re-specify the values of N and K jp in Eq.(7),and re-solve the inventory policy model.This,in turn,leads to a new approximation of the safety stock inventory cost that can be used to re-solve the location model.These iter-ations continue until the number and locations of the DCs do not change from one iteration to the next.The general formulation of the®xed-charge facility location model is as follows(see Daskin, 1995):minXk f k X k /XiXkG i d ik Y iks:t:XkY ik 1V iY ik6X k V i;kX k P f0;1g V kY ik P0V i;k;8where f k is the®xed cost of locating a facility at candidate site k,G i the demand at location i,d ik the distance from demand location i to candidate site k,/the cost per unit distance per unit demand,X j1if a facility is to be located at candidate site k,and0otherwise,and Y ik is the fraction of demand at location i which is served by a facility at k.432L.K.Nozick,M.A.Turnquist/Transportation Research Part E37(2001)425±441In Eq.(8),the candidate facility sites have been indexed by k .Out of this set of candidate sites,some number N will be chosen to be opened,and we will then index the open sites by j 1;...;N .The demand at location i ,denoted G i in Eq.(8),represents the aggregation (across products)of the demand for retail location i during a speci®ed time period.In Section 3,we de®ned k ip as the demand rate for product p at location i .The location model (8)is a static model,so if we adopt the convention that the total demand represented in Eq.(8)is over one time period as used in the rate speci®cation,then G i P p P P k ip .The ®xed-charge location model trades o the costs of opening facilities (the ®rst term in the objective function)against the transportation costs of serving demand from them (the second term in the objective function).In general,we can reduce the transportation costs by opening more facilities,because it is then more likely that each retail demand location can be served from a DC that is closer to it.However,opening more facilities increases the total facility cost.A vital element in our use of this formulation is the inclusion in the f k term the cost of safety stock in-ventory at the facilities and other ®xed costs which might be associated with activating a potential facility site.Many solution procedures have been developed for the ®xed-charge location model,among them a variety of greedy heuristics including the add,drop,and exchange heuristics;Lagrangian relaxation;and branch and bound (Mirchandani and Francis,1990;Daskin,1995;Dresner,1995).For our analysis we have used a hybrid heuristic (a combination of a greedy add and an im-provement algorithm)as discussed by Daskin (1995).The intuitive basis for this algorithm is to add facilities until the marginal reduction in transportation cost cannot overcome the incremental ®xed cost,and then to search for an improved solution by exchanging subsets of facility sites that have been selected for subsets of the sites that have not been selected.This procedure can produce near-optimal solutions to the ®xed-charge location problem quite quickly,even with relatively large sets of potential locations.Since the location model operates with discrete variables,obtaining ``convergence''in the it-erative algorithm that alternates between solving the location problem and solving the inventory policy problem involves ®nding a safety stock inventory cost that produces the same integer number of DC locations as in the previous iteration.We do not have to converge to a precise estimate of the inventory costs ±only to one that is close enough that the location model does not change the number of DCs selected.Thus,our search is for an inventory cost representation that is ``consistent''with the number of DC locations chosen by the location model,and we can tol-erate some error in this approximation without a ecting the overall solution strategy in any adverse way.Several di erent means for representing the safety stock inventory costs are possible.We discuss two alternatives here,and illustrate the use of one of those alternatives in a case study in Section 6.5.1.Representing inventory costs ±alternative 1Suppose we adopt a decision rule on separating products into two groups based on total volume,as described in Section 4.If the minimum volume for a product to be stocked at the DCs is K min ,we can de®ne a subset of products,P H ,to be stocked at the DCsP H f p j K 0p >K min ;p P P g : 9 L.K.Nozick,M.A.Turnquist /Transportation Research Part E 37(2001)425±441433Initially,the speci®cation of K min is done without knowledge of the number of DCs,so it may not be the ``correct''value,but speci®cation of a trial value allows determination of a trial set of products,P H .If we further assume that the total demand for product p in P H ;K 0p ,is approximately equally divided across all the DCs,and we specify an acceptable stockout level, r p ,to be applied across all DCs for product p (i.e.,r jp s jp r p ;j 1;...;N ),we can use (3)to determine the minimum total stock level, s p ,for product p at each DC (i.e.,s Ãjp s p ;j 1;...;N ).The safety stock at each DC for product p is then s p Àl H 1p K 0p =N ,and the total safety stock across N DCs is N s p Àl H 1p K 0p .Thus s p provides an estimate of the marginal increase in total safety stock across all DCs as the number of DCs increases.Of course, s p is not constant as N changes (because it is calculated from (3)),but it is quite easy to calculate s p values for several values of N and average them,for ex-ample.If the inventory holding cost for product p is h p (assumed to be the same at all locations),then an estimate of the marginal safety stock cost of an additional DC is c K min X p P P Hh p s p :10 The notation c K min )emphasizes that this cost is dependent on the choice of K min which in turn determines the set P H :In the ®xed-charge location model,we then replace f k by f k c K min as the ®xed cost (where f k represents the noninventory ®xed costs for a facility),and solve for a set of locations at which to open DCs.Nozick and Turnquist (1998)show that if the necessary safety stock is calculated based on an equal allocation of demand to each of the DCs,the result is an upper bound on the actual safety stock required for any other assignment of demand to DCs,so this procedure yields a slightly conservative estimate (i.e.,over-estimate)of total safety stock requirements,and hence total safety stock cost.5.2.Representing inventory costs ±alternative 2Suppose we have some trial set of DC locations,so that we have an estimate of N and K jp for j 1;...;N and p P P .Then we can solve Eq.(7)for each product p to get a speci®cation of the inventory levels s Ã0p ;s Ã1p ;...;s ÃNp .This is,in fact,the standard ``inventory side''of the iterative procedure.Knowing s Ã1p ;...;s ÃNp we can calculate the portion of the total stock for product p that is safety stock at the DCs by computing X N j 1s Ãjp Àl H 1p K jp X N j 1s Ãjp !Àl H 1p K 0p : 11 The second term,l H 1p K 0p ,is the cycle stock which is una ected by changes in the number of DCs.Thus,an estimate of the marginal e ect of another DC on total safety stock for product p is 1=N P N j 1s Ãjp ,and we can estimate the marginal safety stock cost of another DC asc N ;K jp 1N X p P P h p X N j 1s Ãjp : 12 434L.K.Nozick,M.A.Turnquist /Transportation Research Part E 37(2001)425±441。

企业战略管理双语教学老师给的习题

企业战略管理双语教学⽼师给的习题Multiple choiceChapter 11. The prescriptive, deliberate or planned approach views strategic management as a____________A. highly systematized processB. deterministic processC. highly systematized and deterministic processD. consistent pattern of behaviour2. ____________ is used to refer to strategic formulation, implementation and evaluation, with ______________ referring only to strategic formulation.a. Strategic planning; strategic managementb. Strategic planning; strategic processingc. Strategic management; strategic planningd. Strategic management; strategic processinge. Strategic implementation; strategic focus3. What can be defined as the art and science of formulating, implementing and evaluating cross-functional decisions that enable an organization to achieve its objectives?a.Strategy formulationb.Strategy evaluationc.Strategy implementationd.Strategic management4. Conducting research to determine internal strengths and weaknesses is performed during which stage of strategic management? ____________a. Formulationb.Implementationc.Evaluationd.Feedbacke.Goal-setting5. What are the three stages of the strategic management process?a.Conflict, resolution and implementationb.Formulation, implementation and evaluationc.Formulation, execution and rewardd.Formulation, implementation and resolutione.Goal-setting, implementation and feedback6. An important activity in __________ is taking corrective action.a.strategy evaluationb.strategy implementationc.strategy formulationd.strategy leadershipe.all of the above7. __________ means mobilizing employees and managers to put strategies into action.a.Formulating strategyb.Strategy evaluationc.Implementing strategyd.Strategic advantage8. __________ is not a strategy-implementation activity.a.Taking corrective actionsb.Establishing annual objectivesc.Devising policiesd.Allocating resourcese.Motivating employees9. __________ skills are especially critical for successful strategy implementation.a.Interpersonalb.Technicalc.Conceptuald.Thinkinge.Marketing10. Strategy evaluation is necessary becausea. internal and external factors are constantly changing.b. the SEC requires strategy evaluation.c. competitors change their strategies.d. the IRS requires strategy evaluation.e. firms must take corrective actions.11. Which of these is often considered the first step in strategic planning? _________a.Developing a vision statementb.Establishing goals and objectivesc.Making a profitd.Developing a mission statemente.Determining opportunities and threats12. What are enduring statements of purpose that distinguish one business from other similarfirms? _________a.policiesb.mission statementsc.objectivesd.rulese.employee conduct guidelines13. Which of the following is not included in the strategic management model?a. Measure and evaluate performance.b. Perform internal research to identify customers.c. Establish long-term objectives.d.Implement strategies.e. Develop mission and vision statements/doc/9a441fe919e8b8f67c1cb9c0.html ually, external opportunities and threats are:A.uncontrollable by a single organization.B.controlled by governments.C.not as important as internal strengths and weaknesses.D.key functions in strategy implementation.E.key functions in strategy exploitation.15. Military strategy is based on an assumption of __________, whereas business strategy isbased on an assumption of __________.a.conflict; cooperationb.conflict; competitionc.cooperation; conflict/doc/9a441fe919e8b8f67c1cb9c0.html petition; conflicte.cooperation; competition16. Competence Based Approach argues that/doc/9a441fe919e8b8f67c1cb9c0.html petitive advantage arises from an organization’s internally developed corecompetence rather than from its environment/doc/9a441fe919e8b8f67c1cb9c0.html petitive advantage arises from positioning a firm to take advantage ofopportunities and overcome or circumvent threats/doc/9a441fe919e8b8f67c1cb9c0.html petitive advantage arises from cooperation/doc/9a441fe919e8b8f67c1cb9c0.html petitive advantage arises from opportunities17. Resource-based view approach argues that an organization should exploit its_________relative to _________ in the external environmenta.position; opportunitiesb.basic competencies; opportunitiesc.financial assets; opportunitiesd.core competencies; opportunitiesChapter 21. The purpose of the mission statement is to communicate to_________a.all shareholdersb.employeesc.all stakeholdersd.managers2. A good mission statement should _________a.define what the organization isb.limit to exclude some venturesc.give detail plans of allocating resourcesd.be broad enough to allow for growthe.distinguish a firm from all others3. According to McGinnis, a mission statement should be all of the following except:a. it should be specific enough to control creative growth.b. it should be stated in clear terms.c. it should distinguish an organization from all others.d. it should define what an organization is.e. it should serve as a framework for evaluating both current and prospective activities.4.It is the _________who determines what a business is.a. president.b. customerc. stakeholder.d. CEO.5.What the customer buys and considers value is alwaysa. price.b. functionc. technology.d. utility6 . Which mission statements are good mission statement _________a.AT&T’s (美国电报电话公司)mission statement focuses oncommunicationb.Exxon’s （埃克森⽯油公司）mission statement focuses on oil and gasc.Union Pacific’s （太平洋联合铁路公司）mission statement focuses on transportationd.Universal Studios’（环球电影公司）mission statement focuses on movies Chapter 31. Financial crisis that reverberated around the world is belong toa. far environments’ factorsb. near environments’ factorsc. internal environments’ factorsd. industrial factors2.Three broad ways that clusters affect competition: _________a. Increasing the productivity of companies based in the areab. Driving the direction and pace of innovationc. Stimulating the formation of new businesses within the clusterd. Bringing entry barriers to the area3.Which of the following choices does not belong to industry properties_________?a.Economies of Scaleb.Barriers to market entryc. A firm’s core competenced.Product differentiatione.Level of competitiveness4. According to I/O theorists, which of the following contributes least to firm performance?a.Economies of scaleb.Barriers to market entryc.Product differentiationd.Internal resourcese.Level of competitiveness5. __________ is not part of an external audit.a. Analyzing competitorsb. Analyzing the firm’s financial ratiosc. Analyzing available technologiesd.Studying the political environmente.Analyzing social, cultural, demographic and geographic forces6. When interest rates rise, discretionary⾃由决定的income ______, and the demand fordiscretionary goods ______.a.rises; risesb.declines; risesc.rises; fallsd.declines; fallse.stays the same; rise7. When an industry relies heavily on government contracts, ______ forecasts can be the most important part of an external audit.a.economicb.politicalc.technological/doc/9a441fe919e8b8f67c1cb9c0.html petitivee.multinational8. Technological advancements can create new ______ advantages that are more powerful than existing advantages.a.economicb.socialc.environmental/doc/9a441fe919e8b8f67c1cb9c0.html petitive/doc/9a441fe919e8b8f67c1cb9c0.html parative9. The Internet is changing the nature of opportunities and threats by doing all of the following except:a.altering the life cycles of products.b.decreasing the speed of distribution.c.erasing limitations of traditional geographic markets.d.creating new products and services.e.changing the historical trade-off between production standardization andflexibility.10. Intensity of competition _______ in lower-return industries.a.is lowestb.is non-existentc.is highestd.is not importante.fluctuates11. Five competitive forces, according to Michael Porter, create vital opportunities and threatsto organizations. Which of the following is not a competitive force?a. New entrantsb. Rivalry among existing firmsc. Bargaining power of unionsd. Bargaining power of supplierse. Bargaining power of buyers12. ________, according to Porter, is usually the most powerful of the five competitiveforces.a. Potential development of substitute productsb. Bargaining power of suppliersc. Bargaining power of consumersd. Rivalry among competing firmse. Potential entry of new competitors13. Whenever new firms can easily enter a particular industry, the intensity of competitivenessamong firms______a.stays the same.b.increases.c.decreases.d.neutralizes.e.Fluctuates14. If suppliers are unreliable or too costly, which of these strategies may be appropriate?a. Horizontal integrationb. Backward integrationc. Market penetrationd. Forward integratione. Concentric diversification15. Bargaining power of consumers is ______ when the products being purchased are standard or undifferentiated.a. marginalb. lowc. highd. negativee. not necessary16. Globalization of industries is occurring for all of these reasons except: ______a. a worldwide trend toward similar consumption patterns.b.the emergence of global buyers.c. a worldwide trend toward different consumption patterns.d.e-commerce and the instant transmission of money and information across continents.e.the emergence of global sellers.17. ___________ is the first step in designing an EFE Matrix.a. Identifying key external factors in the industryb. Summing the weighted score for each competitorc. Calculating the sales of each competitord. Drawing the horizontal and vertical lines for the matrixe. Determining four competitors18. W hat is the range for a firm’s total weighted score in an External Factor Evaluation Matrix?a. 0 to 5b. 0 to 4c. 1 to 5d. 1 to 4e. 0 to 1019. One difference between CPM and EFE is thata. CPM includes both internal and external issues.b. the weight and total weighted score mean opposite.c. CPM ratings range from 1 to 10.d. CPM is performed only for the company, whereas EFE is performed for both the company and the competitors.e. CPM is only used in small firms20.Strategic groups of firms within an industry follow ___________ or have very___________ dimensionsa. the same strategies, similarb. different strategies,differentc. the same strategies, differentd. different strategies, similar21.Potential development of substitute products will increase when consumer’s switching costs ___________a. increaseb. decreasec. do not changed. become highChapter 41. There are three activities in the internal Analysis process___________a. Resources, capabilities/competencies，core competencies analysisb. Value Chain analysisc. competitor analysisd. Comparative analysis2. A competence is an attribute or collection of attributes possessed by ___________of the firms in an industrya. fewb. severalc. manyd. all or most3. Resources employed by a firm includes ___________a. tangible resourcesb. competitive resourcesc. intangible resourcesd. human resources4. ___________and ___________do not belong to intangible resourcesa. Financial Resourcesb. Technological Resourcesc. Reputationd. Physical Resources5. Which one of the following are tangible resources?a. Financial Resourcesb. Technological resourcesc. Reputationd. Human resources6. _______ exemplifies the complexity of relationships among the functional areas of business. /doc/9a441fe919e8b8f67c1cb9c0.html ernment auditb.External auditc.Financial ratio analysisd.Environmental scanninge.Distribution strategy7. Which of the following are primary activities in a firm’s value chain___________?a. inbound logisticsb. outbound logisticsc. marketing & salesd. procuremente. operations8. Which of the following are not support activities___________?a. technology developmentb. outbound logisticsc. human resource managementd. firm infrastructuree. procurement9.Firm infrastructure consists of a number of activities including ___________a. general managementb. finance & accountingc. legal & government affairsd. quality managemente. planning10. The initial step to implementing value chain analysis is___________a.attaching a cost to each discrete activity.b.establishing costs in terms of time.c.establishing costs in terms of money.d.dividing a firm’s operations into specific activities or business processes.11. In t he “power law” formula y = ax b , ‘a’ representsa. the labor hours required to build unit #xb. the theoretical labor hours required to build the first unit producedc. the rate of learningd. the number (count) of an item in the production sequence12. According to the learning curve theory, when output or production __________, the reduction in time per unit affected by the learning curve ratea. doublesb. triplesc. is four times to the initial oned. is five times to the initial one13.Learning rate is not useful when ___________a. production is sporadicb. there is no way to improve the production ratec. production quantities are very smalld. rules & regulations limit the production ratee. each item produced is significantly different from the preceding item14. In an IFE matrix, rating number “3” represents ___________a. major weaknessb. minor weaknessc. minor strengthd. major strength15. In an IFE matrix, rating number “2” represents ___________a. major weaknessb. minor weaknessc. minor strengthd. major strength16. If a firm’s total weighted score is 2.1 in an IFE matrix, it indicates that ___________a. the firm is being weak internallyb. the f irm’s strategies is not capitalizing on opportunities or avoiding threatsc. the firm is being a strong internal positiond. the f irm’s response is outstanding to threats and weaknessesChapter5-61. Corporate strategy is ___________a. more detailb. more value orientedc. more conceptuald. concerned with the whole firm2. A firm directs its resources to the profitable growth of a single product, in a single market, with a single dominant technology. The firm pursues___________a. diversificationb. horizontal integration Strategyc. vertical integration Strategyd. concentration strategy3.If a firm’s present suppliers are expensive and unreliable in meeting the firm’s needs forparts, components and/or raw materials, it should pursue a ___________a. concentration Strategyb. horizontal integration Strategyc. backward integration Strategyd. forward integration Strategy4. An example of _______ strategy is establishing Web sites to sell products directly toconsumers.a. backward integrationb. product developmentc. forward integrationd. horizontal integration5. A _______ strategy seeks to increase market share of present products or services in present markets through greater marketing efforts.a. market penetrationb. forward integrationc. market developmentd. product development6. Adding new, unrelated products or services for present customers is called______a. forward integration.b. concentric diversification.c. conglomerate diversification.d. horizontal diversification7. Backward integration is effective in all of these except:a. when an organization competes in an industry that is growing rapidly.b. when an organization has both capital and human resources to manage the newbusiness of supplying its own raw materials.c. when an organization needs to acquire a needed resource quickly.d. when the advantage of stable prices are not important.8. When a US company first begins to export to India, it is an example ofa. market developmentb. market penetrationc. product developmentd. . horizontal integration.9. When an organization competes in an industry characterized by rapid technologicaldevelopments, _______ is an appropriate strategy.a. retrenchmentb. product developmentc. backward integrationd. market penetration10. _______are terms that describe diversification strategiesa. Concentric diversificationb. conglomerate diversificationc. vertical diversificationd.horizontal diversification.11. Adding new, unrelated products or services is calleda. horizontal diversification.b. concentric diversification.c. backward integration.d. conglomerate diversification.12. An airline eliminating service at 10 major cities to financially survive is an example of______a. divestiture.b. backward integration.c. liquidation.d. retrenchment13. When a division is responsible for an organization’s overall poor performance, _________ strategy should be implemented.a. backward integrationb. divestiturec. forward integrationd. cost leadershipe. concentric diversification14.Selling all of a company’s assets in parts for their tangible worth is called_________a. joint venture.b. divestiture.c. concentric diversification.d. liquidation.e. horizontal integration15.Defensive strategies includes_________a. retrenchmentb. divestiture.c. diversification.d. liquidation.16. __________ is effective when the stockholders of a firm can minimize their losses by selling the organization’s assets.a. Integrationb. Differentiationc. Diversificationd. Liquidation17.Ways to pursue Differentiation successfully: ________a. creating products which are superior to competitorsb. building superior distribution channelsc. offering superior after sales serviced. creating a strong brand name through design, innovation, advertising, and so on18. Mergers and acquisitions are created for all of the following reasons except to ________a. gain new technology.b. reduce tax obligations.c. gain economies of scale.d. increase its number of employees/doc/9a441fe919e8b8f67c1cb9c0.html prehensive Strategy-Formulation Framework includes: ________a. the Input Stageb. the Matching Stage.c. the Decision Stage.d. the output Stage.20.Which of the following are tools in the matching stage________a. SWOT Matrixb. SPACE Matrixc. BCG Matrixd. IE Matrixe. CPM21.I mproving internal weaknesses by taking advantage of external opportunities is________strategiesa. WOb. STc. SOd. WT22.Two External Dimensions in SPACE matrix are ________a. Environmental Stability (ES)b. Industry Strength (IS)c. Financial Strength (FS)d. Competitive Advantage (CA)23.If a financially strong firm that has achieved major competitive advantages in a growing and stable industry, the firm’s directional vector should be located in the________quadrant of SPACE matrixa. aggressiveb. conservativec. defensived. competitive24. A division with a high relative market share position in a low-growth industry can be described as a________a. star.b. cash cow.c.question mark.d.dog.25. When a division of an organization has a high relative market share and is in a fast-growing industry, it is called a________a. star.b. cash cow.c.question mark.d.dog26 Which of these is not an attractive strategy for a cash cow division? ________a. intensive strategy.b. harvestc.divestitured.retrenchment27.If a firm locates in Cells I, II, or IV in IE Matrix, the firm should pursue__________strategya. Grow and build.b. Hold and maintainc.Harvest or divestd.No above allChapter7-81. __________ is included in the decision stage of the strategy formulation framework.a. Internal Factor Evaluation Matrix (IFE)b. Quantitative Strategic Planning Matrix (QSPM)c.BCG Business Portfolio Matrixd.Grand Strategy Matrixe.SPACE Matrix2.Annual Objectives should state __________a. Quantityb. Qualityc.Costd.Timee.Be Verifiable3. Three basic activities of strategic evaluation, review & control __________a. analyzing industry environmentb. Examine the underlying bases of a firm’s strategy/doc/9a441fe919e8b8f67c1cb9c0.html pare expected to actual resultsd.Identify corrective actions to ensure that performance conforms to planse.analyzing financial ratios4. Three steps in evaluation framework __________a. Review underlying basesb. Allocate resourcesc.Measure firm performanced.Take corrective actions5.Balanced Scorecard evaluate strategies from 4 perspectives: __________a. Financial performanceb. Customer knowledgec.Internal business processesd.Learning & growthe.Macro-economic situation6. Three ways to manage conflict__________a. Avoidanceb. Diffusion/doc/9a441fe919e8b8f67c1cb9c0.html petitiond.Coordinatione.Confrontation7. In the process of implementing strategy, change raises anxiety and fear, concerning__________a. Economic lossb. Inconveniencec. Uncertaintyd Break in status-quoe. improving working condition8. In the process of implementing strategy, change strategies include__________a. Force Change Strategyb. Educative Change Strategyc. integration strategyd diversification strategye. Rational or Self-Interest Change StrategyTrue/False(T)Strategy formulation, implementation and evaluation activities occur at three hierarchical levels in a large diversified organization: corporate, divisional and functional(T)In order for a firm to achieve sustained competitive advantage, a firm must continually adapt to changes in external trends and events and effectively formulate, implement, and evaluate strategies that capitalize upon those factors.Chapter 1-21.(T) By exploring, learning and piecing together a consistent pattern of behaviour over time, an organization may arrive at the same position as if it had planned everything in detail2. (T) A clear vision provides the foundation for developing a comprehensive mission statement3. (F) Mission means “What do we want to become?”4. (T) Clear vision & mission are needed before alternative strategies can be formulated andimplemented5. (F) Participation from diverse managers is not important in developing the mission.6. (T) The vision statement should be short, preferably(更适宜) one sentence7. (F)If an organization chooses to have both a mission and a vision, the mission statement should be established first, as mission identifies where we are and vision would indicate where we want to goChapter 31.(F)External Audit is t o develop an exhaustive list of every possible factor that could influence the business is the aim of external audit.2. (F)Tourism-oriented firms in the United States are hampered(受妨碍) when the value of the dollar falls3. (T) The Internet is changing the very nature of many industries by altering product life cycles and changing the historical trade-off between production standardization and flexibility4. (T)New firms sometimes enter industries with higher-quality products, lower prices and substantial marketing resources, even though there are numerous barriers to entry.5.(T)The impact of natural events upon business activity can be very powerful and difficultto predict or avoid6. (T)Both a Competitive Profile Matrix and an EFE Matrix have the same meaning in the weights, ratings and total weighted scores.7. (T) The critical success factors in a Competitive Profile Matrix are often the same as those in an EFE Matrix.Chapter 41. (T) The process of performing an internal audit, compared to the external audit, provides more opportunity for participants to understand how their jobs, departments and divisions fit into the whole organization.2. (T) The value chain is composed of value-adding activities and margin3. (T) Value Chain Analysis can enable a firm to better identify its own strengths and weaknesses especially as compared to competitors’ Value Chain Analyses4.(T) Firm infrastructure can be a powerful source of CA5. (T) The value chain is not a collection of independent activities but a system ofinterdependent activities.6. (T)Internal Factor Evaluation Matrix is a summary step when conducting an internal strategic-management audit7. (T)In competitive terms, value is the amount buyers are willing to pay for what a firm provides them8(F)The value chain is a collection of independent activities9. (T)The learning curve describes the relationship between a firm’s cumulative output and amount of inputs needed to produce a unit of output10.(T)100% learning rate means no learning at all11. (F)In industry, S typically ranges from 40% to 100%12.(F)The learning effect can lead to very large reductions in cost and it depends on the size of the individual firm13.(T)The rate of learning depends on factors such as the quality of management and the potential of the process and productsChapter 5-61. (T)Business strategy ( competitive strategy)is the determination of how a company will compete in a given business and position itself among its competitors2. (F) In a changing environment, a firm committed to concentrated growth faces low risks3. (F) Forward integration is a strategy of seeking ownership or increased control of a firm’s suppliers4. (F)Gaining ownership or increased control over distributors or retailers is called backward integration strategy5. (T)The increased use of horizontal integration as a growth strategy6. (T) Introducing present products into new geographic areas is market development7. (T) An appropriate strategy when an organization has excess production capacity is market development8. (T) Liquidation is often appropriate when retrenchment and divestiture have failed9. (F)According to Porter, strategies allow organizations to gain competitive advantage from three different bases: cost leadership, differentiation and integration10. (T) For consumers who are price sensitive, cost leadership emphasizes producing standardized products at very low per-unit cost11. (T)When an acquisition is not desired by both parties, it is called a takeover or hostile takeover12. (T) Not all M & As are effective and successful13. (T) M & As can yield great benefits, but the price and reasoning must be right14. (T) Business is both co-operation and competition15. (F)Companies are avoiding outsourcing more and more because it is more expensive than traditional methods and it does not allow a firm to concentrate on core competencies16. (T) Merger & Acquisitions can yield great benefits, but the price and reasoning must be right17 (T)According to Porter, a firm that engages in each generic strategy but fails to achieve any of them is “ stuck in the middle”.18. (T)BCG Matrix enhances multi-divisional firm in formulating strategiesChapter 7-81. (T)Implementing strategy affects an organization from top to bottom2. (T)Changing a firm’s culture to fit a new strategy is usually more effective than changing a strategy to fit an existing culture3.(T)Strategy evaluation is v ital to the organization’s well-being4.(T)Strategy should not present inconsistent goals & policies5. (F) In terms of number of employees, restructuring involves increasing the size of the firm6. (F)The overall aim of the Balanced Scorecard is to balance financial objectives with strategic objectives7. (T)There must be a translation of strategic thought into strategic action8. (F)Reengineering is characterized by many strategic decisions9. (F)Restructuring is characterized by tactical decisions10.(T)In the Balanced Scorecard, the Learning & Growth Perspective is the foundation of anystrategy and focuses on the intangible assets of an organizationEssay QuestionsChapter 1-21. Explain the relationship between strategic management and competitive advantagefor firms. How can a firm achieve sustained competitive advantage?Ans: Strategic management is all about gaining and maintaining competitive advantage.Competitive advantage is anything a firm does especially well compared to rival firms.When a firm can do something that rival firms cannot do, or owns something that rival firms desire, that can represent a competitive advantage. Getting and keepingcompetitive advantage is essential for long-term success of an organization. A firm must strive to achieve sustained competitive advantage by (1) continually adapting to changes in external trends and events and internal capabilities, competencies andresources, and by (2) effectively formulating, implementing and evaluating strategies that capitalize upon those factors.战略管理的⽬的就是使企业获得并保持竞争优势。

估价问题

经验方法麻省理工14.771/哈佛 2390b2002年秋这本册子的目的是为了阐述应用经济学所运用到的一些最普遍的经验方法。

对于计划评审技术和自然实验等方法来说，最好的参考书来自Angrist and Krueger（1999）和Mayer（1999）。

Angrist and Krueger（1999）包含更多的资料也比本书更为详细，对于打算写经验发展和公共财政的劳动力等方面论文的同学更为合适。

1．估价问题在发展经济学、劳动经济学和公共财政学中所运用到的经验方法，已经被发展用来回答一些反事实的问题。

如果一个人倾向于选择政策T，会对她的行为有何影响？（例子：如果边际税率降低她是否会工作得更多，如果她不去上学是否会赚得更少，如果在村里有个免疫中心她是否会更有可能接受免疫？）这里有个例子来说明计划评审技术中的基本难点：我们以代表有教科书的给定学校i中学生的平均考试成绩，以代表没有教科书的学校i的平均成绩。

两者之间的差额无疑更让我们感兴趣，因为它反映了拥有教科书所带来的效用。

问题：我们不可能找到一个学校i同时出现有教科书和没有教科书两种情况。

我们该怎么办？我们永远不能知道教科书对特定的一个学校的效用但我们会希望知道它对所有学校的平均效用。

假想我们能够拿到一个地区很多学校的数据。

一些学校有教科书而一些没有。

对两组数据分别求平均值，并计算有教科书和无教科书学校的平均考试成绩之差。

即：D=E[|有教科书的学校]—E[|没有教科书的学校]=减去和加上，我们得到：前面一段是我们要分离出来的处理效果（对被处理数据处理后的效果）：在被处理过的学校中，教科书会起到什么样的影响？差额是选择上的偏见。

它告诉我们，除了教科书的影响，还可能有系统性的差异存在于有教科书的学校和其他学校之间。

经验方法试图解决这个问题。

2．随机化的评估要评估政策X对产出Y影响，最理想的方法是随机实验。

可参考Rosenbaum（1995）在一个随机实验当中，从总体中选出N个值组成样本（注意这个样本不一定是随机的，因为在选择过程中可能会有一些观测的误差）。

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INTRODUCTION
A two-echelon inventory system is considered consisting of one central warehouse and an arbitrary number of retailers with identical ordering batch sizes. The inventory control policy is assumed to be a continuous review (R; Q) policy in all installations, which means that when the inventory position reaches a predetermined value of R, an order of size Q is placed. The demand processes for a consumable (not repairable) item are assumed to be independent Poisson and unsatis ed demands to be lost in all retailers. The transportation time of each order placed by the retailers is assumed to be constant. A constant lead time is assumed for replenishing the warehouse orders from an external supplier and unsatis ed retailer orders to be backordered in the warehouse and all backordered orders are lled according to a FIFO-policy. The reorder point and batch size of the warehouse are assumed to be integer multiples of the retailers identical batch size. One of the oldest papers in the eld of continuous review multi-echelon inventory systems is a basic and famous one written by Sherbrooke 1] in 1968. He assumed (S 1; S ) policies in a Depot-Base system for repairable items in the American air force and could
106 policy, independent Poisson demands in the retailers, a backordered demand during stockouts in all installations and constant lead times. Axsater 9] proposed exact and approximate methods for evaluating the previous system for the case of a general batch size in all installations but with identical retailers. For the case of non-identical retailers and a general batch size, Axsater 10] proposed methods for the exact evaluation of two retailer cases and an approximate evaluation for the case of more than two retailers. Forsberg 11] presented a method for exactly evaluating the costs of a system with one warehouse and a number of di erent retailers using another approach. The common assumption of the above papers is that demands during stockout in the retailers are backordered. However, on some conditions, demands may be lost. Andersson and Melchiors 12] have proposed an approximate method for the case of lost sales when the inventory control policy is (S 1; S ) in all installations (one warehouse and multiple retailers) and unsatis ed demands are lost in the retailers. They also introduced the cost evaluation of such a system in case of a general batch ordering policy as a future eld of research. This is what is being considered in this paper. The contents of this paper are now outlined. First, a detailed problem formulation is given and the review of two special single echelon problems that are referred to later are presented. Then, it will be explained how to overcome the two important complexities of the model. After that, the approximate total cost of the system is presented and discussed for nding reorder points. Finally, numerical results and some conclusions and further research opportunities are presented.
*. Corresponding Author, Department of Industrial Engineering, Sharif University of Technology, Tehran, I.R. Iran. 1. Department of Industrial Engineering, Sharif University of Technology, Tehran, I.R. Iran.
M.R. Akbari Jokar and M. Seifbarghy
1
The inventory system under consideration consists of one central warehouse and an arbitrary number of retailers controlled by a continuous review inventory policy (R; Q). Independent Poisson demands are assumed with constant transportation times for all retailers and a constant lead time for replenishing orders from an external supplier for the warehouse. Unsatis ed demands are assumed to be lost in the retailers and unsatis ed retailer orders are backordered in the warehouse. An approximate cost function is developed to nd optimal reorder points for given batch sizes in all installations and the related accuracy is assessed through simulation.
approximate the average inventory and stockout level in the bases. The result of this paper has been used by many subsequent researchers because it uses an e cient approximation for the lead time of the bases (which is usually one of the complexities of multiechelon systems). However, other papers, like 2], studied Sherbrooke's model by changing some of its critical assumptions and gained some more interesting results. Continuous review models of multi-echelon inventory systems in the 1980's concentrated more on repairable items in a Depot-Base system than on consumable items. For example, Graves 3] worked on the determination of the stocking levels in such a system, Moinzadeh and Lee 4] considered the issue of determining the optimal order batch size and stocking levels at the stocking locations by using a power approximation and Lee and Moinzadeh 5] generalized previous models on multi-echelon repairable inventory systems to cover the cases of batch ordering and batch shipment. On consumable items, Deuermeyer and Schwarz 6] proposed a simple approximation for a complex multi-echelon system (one warehouse and multiple retailers) assuming the backordering of stockouts in all installations with a batch ordering policy. Svoronos and Zipkin 7] proposed several re nements by considering second-moment information (standard deviation as well as mean) in their approximations. In the 1990's, Axsater 8] provided a simple recursive procedure for determining the holding and stockout costs of a system, consisting of one central warehouse and multiple retailers with an (S 1; S )