Implementation of Spreadsheet Modeling to Compare the Annual Energy Performance and Cost o

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5Spreadsheet-Aided Dryer DesignZ.B.Maroulis,G.D.Saravacos,and Arun S.Mujumdar CONTENTS5.1Introduction (121)5.2Principles and Techniques of Spreadsheet-Aided Process Design (121)5.3Design of a Conveyor Belt Dryer (126)5.3.1Process Description (126)5.3.2Process Model (126)5.4Excel Implementation of a Belt Dryer Design (127)Nomenclature (129)References (134)5.1INTRODUCTIONSpreadsheet software has become an indispensable tool for engineers,because of the availability of per-sonal computers,ease of use,and adaptability to many types of problems.Spreadsheet software has achieved great popularity because of its availability for microcomputers at reasonable cost,the ease of learning and using the software,and itsﬂexible appli-cations to many problems.Furthermore,general-purpose spreadsheet soft-ware can be used effectively in process design(Maroulis and Saravacos,2003).For example,Microsoft Excel with Visual Basic for Applications is an effective tool for process design.Spreadsheets offer sufﬁ-cient process model‘‘hospitality.’’They are con-nected easily and online with charts and graphic objects,resulting in powerful and easy-to-use graph-ical interfaces.Excel also supports mathematical and statistical tools.For instance,Solver is an excellent tool for solving sets of equations and performing optimization.Databases are effectively and easily ac-cessed.In addition,Visual Basic for Applications offers a powerful object-oriented programming lan-guage,capable of constructing commercial graphics interfaces.It is the objective of this chapter to present step-by-step procedures in order to allow application of various dryer models into the Excel environment. This chapter refers to two main topics.The principles for solution of a process design problem are presented ﬁrst and then the principles for Excel implementation are described.The reader needs to become familiar with the following topics regarding Excel software,using the related literature:.Modeling and spreadsheets.Analyzing the Solver.Sensitivity analysis using Excel tables.Controls and dialog boxes to input data.Graphics to get the results.Databases.Visual Basic as a programming language5.2PRINCIPLES AND TECHNIQUES OFSPREADSHEET-AIDED PROCESS DESIGN Computer-aided design is based on computer simu-lators,whereas computer simulators are based on process modeling.The basic terms,such as modeling, simulat i on, and de s ign, are deﬁ n ed in Table 5.1. Mo d-eling is the procedure of translating the physical laws of a process to mathematical equations to analyze or design the process.Simulation is the appropriate soft-ware,which predicts the real performance of a pro-cess.It is based on mathematical modeling plus the appropriate graphics interface in a computer environ-ment.Design is a procedure of sizing and rating a process in order to achieve speciﬁc goals,such as economic production,product quality,and protection of the environment.Modeling and simulation are useful tools in process design. Table 5.2 summ a rizes a step- b y-step procedu r e for pr o cess modeli n g, wher e as Table 5.3summ a rizes a step- b y-step procedure for process sim u-lation. These steps are further ana l yzed.The equations constituting a model describe the physical laws, which apply to the process. They are derived from material and energy balances, thermo-dy n a m ic e q ui l i b r i um r e la t ions h i p s , t r a n spor t phe n om -ena, geometry, equipment characteristics, etc. Generally some assumptions are also built into the model.A degrees -of-fre e dom an a lysis is shown in Table5.4 and in Figure 5.1. Suppos e that M variab l es are incorporated into the mathematical model of N equa-tions; generally,M is greater than or equal to N, and the difference M–N corresponds to the degrees of freedom of the process . The degrees of freedom is ch a racteris -tic of the process . In pro c ess design, some varia b les have given values , due to the de s ign speciﬁca t ions , and the remaind e r corres p onds to design variab l es.The number of design varia b les is charact e ristic of the problem . Several different pro b lems c o uld be de -ﬁned for every process (see, for example ,Table 5.5) . The values for the design varia b les are decided by the design engineer . The remai n der NÂN set of eq u ations is solved by using mathe m ati c al techni q ues. In chem-ical an d food engineer i ng the resul t ing syst e m is sparse , that is every varia b le ap p ears in a few eq -uations . In that case the system can be solved sequenti a lly (down trian g le matrix) or by using a few trial varia b les.The ab o ve ap p roach is suit a ble for impl e ment a-tion in a spreads h eet en v ironmen t. The resul t ing simulat o r has generally the outline present e d in Figure 5.2. Four diff e rent units are dist i nguished , with each one developed in a different sheet (Maroul i s and Saravacos , 2002).The ‘‘Proc e ss Mod e l Worksheet ’’ is the he a rt of the syst e m calcul a tions.It co n tains the proce s s model. When no interactio n s are ne e ded, the mod e l solution uses only works h eet functi o ns. In that case, when any change in inpu t variab l es (free va r iables) occu r s, the solution is obtaine d automa t ically on this works h eet.Since the use of the simulator requ i res the solution of diff e rent pro b lems, several different problem s are formu l ated in the ‘‘Problem Solution Visual Basic Modu l e.’’ Their solution is based on the sim p lest problem of the pro c ess model worksh e et above, and uses the Solver or the Goal Seek utilities of Excel via a Visual Basic program,to obtain a solution for the alternative problems.All technical and required data are retrieved from the‘‘Database worksheet,’’which contains all the required information in the form of‘‘data lists.’’These data are extended and modiﬁed via appropriate dialog boxes.‘‘Graphics interface worksheet’’is a user-friendly way for human–machine communication.It usually consists of three parts:(a)Problem speciﬁcations:The speciﬁcations and the required data for the problemTABLE 5.1Basic Deﬁni t ionsModeling: is the procedure to translate the physical laws of a process to mathematical equationsSimulation : is the appropriate software which guesses the real performance of a processDesign: is a procedure to size and rate a process in order to obtain a speciﬁc goalSizing:given the process speciﬁcations calculate the equipment size and characteristicsRating:given the process speciﬁcations and the equipment size and characteristics calculate the operating conditionsTABLE 5.2Process Modeling1.Process model formulation2. Degrees-of-freedom analysis3. Alternative problem formulations4.Problem-solution algorithm5.Cost estimation and project evaluation analysis6.Process optimization TABLE 5.3Process Simulation Procedu r e in a Sp r eadshee t Enviro n ment1. Model development in a spreadsheet2. Implementation of alternative problem solutions or optimizationprocedures3.Development of graphics interfaceTABLE 5.4Degrees- o f-Fre e dom AnalysisTotal number of variables MTotal number of equations NDegrees of freedom F ¼M–N Process characteristic Degrees of freedom FProblem speciﬁcations KDesign variables D¼F–K Problem characteristicto be so l ved are entere d by the use r or estimat e d from the databas e s. Data are inser t ed via dialog box e s or buttons for changing some impor t ant magn i tudes. (b)Problem- t ype selection: The type of pro b lem to be solved is selec t ed via buttons . (c) Resul t s present a -tion: The resul t s are obtaine d automa t ica l ly, an d are present e d in the form of table s or ch a rts. Since these charts are updated automa t ica l ly, the user has at his disposa l all the infor m ation ne e ded for sizi n g, rati n g,sensitiv i ty an a lysis, or compari s on of alte r native solution s .The foll o wing steps co m prise an Excel impl e men-tation proced u re:1. Workboo k preparation2. Process mo d eling in a sp r eadsheet3. Using ‘‘Solver’ ’ for process optimizat i on4. Using graphs and table s for present a tion of the results5. Introduc i ng dialog box e s and control s to mo d -ify data6. Toward a n integ r ated graphic s inter f ace Step 1: Workbook PreparationCreate a new workbook an d name it to de s cribe the process , e.g., ‘‘BeltDr y er.xls.’’ Insert an d na m e blank sheets are present e d in Tabl e 5.6.Step 2: Process Modeling in a SpreadsheetInto the spreads h e e t ‘‘Proc e ss’’ consider seven separ-ate ranges, as it is present e d in Table 5.7.Eac h range consis t s of three columns and severa l rows, one row for every varia b le in the range. In each range the ﬁrst column contai n s the variable names,the second the varia b le values or variab l e form u las,and the thir d the units use d . Name all cells in second columns accordi n g to the names in the ﬁrst c o lumn.(You can use the ‘‘Ctrl þS hift þF 3’’ option .)TABLE 5.5Some Typical Problem sDirectGiven the characteristics of input streamsthe equipment characteristics the operating conditionsCalculate the characteristics of the output streams DesignGiven the characteristics of input streamsthe characteristics of output streamsCalculate the equipment characteristicsthe operating conditions RatingGiven the characteristics of input streamsthe characteristics of output streams the equipment characteristicsCalculate the operating conditionsIdentiﬁcationGiven the characteristics of input streamsthe characteristics of output streams the operating conditionsCalculate the equipment characteristicsFIGURE 5.1Degrees-of-freedom analysis.FIGURE 5.2Simulator architecture on a spreadsheet environment.The ranges ‘‘Technical Data,’’‘‘Design Vari-ables,’’‘‘Process Speciﬁcations,’’and ‘‘Economic Data’’contain only data.The ranges ‘‘ProcessModel,’’‘‘Process Constraints,’’and ‘‘Economic Model’’contain formulas.Having inserted data and formulas,the process model implementation has been completed.The resulting spreadsheet ‘‘Process’’looks like that pre-sented in Figure 5.3.The cell ranges can be colored with different colors.The drawn arrows show the information ﬂow in the spreadsheet.The spreadsheet process model is now ready for use.Any changes in process data,economic data,process speciﬁcations,design variables are taken into account and the results are updated immediately.Any optimization technique,graphical or tabu-lated reports,any scenario analysis,or sensitivity an-alysis,any sophisticated graphics interface can be based on the ‘‘Process’’spreadsheet.Some examples follow.Step 3:Using ‘‘Solver’’for Process OptimizationCreate a Visual Basic subroutine with the name ‘‘optimum’’in the ‘‘Optimize’’module.The approp-riate code is shown in Table 5.8.TABLE 5.6Sheets in ‘‘BeltDryer.xls’’WorkbookSheet Name PurposeSpreadsheets Process Process model Flow sheet Process ﬂow sheetReport Summary report of results ControlGraphics interfaceVisual Basic Modules Optimize Process optimization subroutinesControlsSubroutines for dialog boxes and controls Dialog box sheets Spec Process speciﬁcations Tech Technical data CostEconomical dataTABLE 5.7Cell Content in ‘‘Process’’SpreadsheetRange Name Content Technical data Data Design variablesData Process speciﬁcations Data Economic data Data Process modelFormulas Process constraints Formulas Economic modelFormulasFIGURE 5.3Model implementation in the ‘‘Process’’spreadsheet.TABLE 5.8Visual Basic Subroutine for Process OptimizationSub optimum()1Sheets(‘‘Process’’).Activate 2SolverReset3SolverOk SetCell:¼Range(‘‘objective’’),MaxMinVal:¼1,ByChange:¼Range(‘‘variables’’)4SolverAdd CellRef:¼Range(‘‘constraints’’),Relation:¼3,FormulaText:¼0#5SolverSolve UserFinish:¼True 6Beep End SubStatement1activates the‘‘Process’’spreadsheet. Statement2resets the Solver.Statement3selects the cell with the name‘‘objective’’to be the ob-jective function[SetCell:¼Range(‘‘objective’’)],re-quires the minimization of the objective function [MaxMinVal:¼2],and selects the range‘‘variables’’to be the decision variables[ByChange:¼Range (‘‘variables’’)].Statement4suggests that all cells in the range‘‘constraints’’[CellRef:¼Range(‘‘constraints’’)] must be greater than[Relation:¼3]zero[Formula-Text:¼0#].Statement5activates the solver toﬁnd the optimum.The above-mentioned cell names must be deﬁned. Thus,in the sheet‘‘Process’’name:.The cells that contain the values of the designvariables as‘‘variables’’.The cells that contain the process constraints as‘‘constraints’’.The cell that contains the proﬁt as‘‘objective’’In the sheet‘‘Process’’insert a new button,name it ‘‘optimizer’’and assign it to the subroutine‘‘opti-mum.’’Press the button‘‘optimizer’’and the optimum is reached in a few seconds.Step4:Using Excel Tables and Charts for Presenta-tion of the ResultsThe process design results can be further analyzed using the tools‘‘Tables’’and‘‘Charts’’supported by Excel.For example,a processﬂow sheet can easily be constructed in Excel as follows:in the sheet‘‘Flow sheet’’draw aﬂow sheet by using the drawing tool-bar.Any information concerning process conditions can be inserted in cells near the desired point of the ﬂow sheet.For each piece of information there need to be three cells,one for the variable name,one for the variable value,and one for the variable units. That is,to insert a streamﬂow rate,select a cell near the icon of the stream arrow and insert the symbolic name of the streamﬂow rate,i.e.,‘‘F¼,’’in a neigh-boring cell insert the formula‘‘¼F’’to get the value from the‘‘Process’’sheet,and in another cell, nearby,insert the units,i.e.,‘‘kg/s.’’You can add any information you like.Any changes in data are up-dated immediately.In order to plot the effect of the design variable (X)on a technical(Y)and an economic(Z)variable the following steps can be used:construct a one-di-mensional Excel table in which the‘‘Column Input Cell’’is the cell with the name‘‘X.’’The second and third output columns refer to the cells‘‘Y’’and‘‘Z,’’respectively.Next construct a‘‘XY(Scatter)’’chart in which theﬁrst column of the table corresponds to x-values and the second to y-values.Similarly,con-struct a second‘‘XY(Scatter)’’chart in which theﬁrst column of the table corresponds to x-values and the third to y-values.Any other tabulated results or desired reports can be easily obtained as follows:select a spreadsheet to incorporate the required information.Insert text or graphics as you like.Get the information from the ‘‘Process’’sheet,as described previously in theﬂow sheet construction procedure.Step5:Introducing Dialog Boxes and Controls to Modify DataA dialog box can be used to modify the values of process speciﬁcations,which are included in the range‘‘Process Speciﬁcations’’in the spreadsheet ‘‘Process.’’In the Dialog Module‘‘db_spec’’insert for every variable one‘‘Label’’(from the toolbar‘‘forms’’)for its description,one‘‘Edit Box’’(from the toolbar ‘‘forms’’)for its value,and one‘‘Label’’for its units. Name all the Edit Boxes with the name of the corre-sponding variable.In the Visual Basic Module‘‘vb_controls’’type a subroutine to use the dialog box in the sheet ‘‘d_spec,’’as described in Table5.9.In the spreadsheet‘‘Process’’insert a button, name it‘‘speciﬁcations,’’and assign it to the subrou-tine‘‘DialogSpeciﬁcations.’’Press the button‘‘speciﬁcations’’and a dialog box appears in order to modify data for process speciﬁcations.A scroll bar can be used for each design variable in order to modify the values of the design variables, which are included in the range‘‘Design Variables’’in the spreadsheet‘‘Process.’’TABLE5.9A Subroutine to Activate the Dialog BoxSub DialogSpeciﬁcations()dbName¼‘‘d_spec’’DialogSheets(dbName).EditBoxes(‘‘W’’).Text¼Range(‘‘W’’).Value DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text¼Range(‘‘Xo’’).Value DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text¼Range(‘‘Yo’’).Value If DialogSheets(dbName).Show ThenRange(‘‘W’’).Value¼DialogSheets(dbName).EditBoxes(‘‘W’’).Text Range(‘‘Xo’’).Value¼DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text Range(‘‘Yo’’).Value¼DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text End IfBeepEnd SubA scrol l bar, in order to ha n dle the va r iable X, can be inserted as follows :.Insert the scrol l bar icon from the too l bar‘‘forms ’’.Insert the mini m um allowabl e value in a cellnamed ‘‘X.m i n’’.Insert the maxi m um allowabl e value in a cellnamed ‘‘X.m a x’’.Insert the coded value in a cell na m ed ‘‘X.C V’’The co d ed value ranges between 0 and 100 and is deﬁned as follows :X.CV ¼ (XÀX.min) /(X.max ÀX min)*1 00.Insert a scroll ba r from the toolbar ‘‘forms’’ andassign the ‘‘Cel l Link ’’ (in the ‘‘Form a t Object’’menu) to the coded value ‘‘X.CV ’’.Repla c e the con t ent of the cell named ‘‘X’’ wi t hthe foll o wing form u la:¼ X.min þX.CV *(X.ma xÀX.m i n)/100It must be noted that the range ‘‘va r iables’’ which is hand l ed by the solver during optim i zation must be redeﬁned to refer to coded values , instead of the ac-tual values . This modiﬁcat i on g u arante e s the prop e r perfor m ance of the optimizat i on and of scrol l bars.Step 6: Toward an Integrated Graphics InterfaceAny desired graphics interface can be developed in the spreadsheet ‘‘Control.’’ It can be constructed as follows:.Draw a proc e ss ﬂow sheet in sheet ‘‘Contr o ls,’’as de s cribed in Step 5.Insert buttons to appear and disappea r the cru-cial graphs.Insert buttons to activate the desired dialog boxes .Insert scrol l bars to modif y the desir e d pro c essvariab l es.Insert buttons to solve different pro b lems, e.g. ,process optimizat i on.The user has now at his dispo s al a process sim u la-tor. He can en t er da t a via scroll ba r s or dialog box e s and observe the resul t s via buttons , which acti v ate the desired grap h s or report s.The graphic s interface could be furt h er impr o ved to loo k professional using appropri a te program m ing code in Visual Bas i c.5.3 DESIGN OF A CONVEYOR BELT DRYER In this section a design app r oach is descri b ed for a conveyo r belt dr y er (Maroul i s an d Sa r avacos , 2003).5.3.1 P R OCESS D ESCRIPTIONA typic a l ﬂow sheet of a con v eyor belt dryer is pre-sented in Figure 5.4. The wet feed at ﬂow rate F (kg/ s db), tempe r atur e T0 (8 C) , and humidi t y X0 (kg/kg db) is dist r ibuted on the belt as it en t ers the dryer. The dried produ c t exits the dry e r at the same ﬂow rate on dry basis F (kg/ s db) , tempe r ature T (8 C), and mois -ture content X (kg/ k g db). The belt is moving a t a velocity u (m/s) and req u ires an elect r ical power E b (kW). The dr y ing air enters the dryer at a ﬂow rate F f (kg/s db),temperature T(8C),and humidity Y(kg/kg db).The drying air temperature is controlled in the heater,and the drying air humidity is controlled through theﬂow rate of the fresh air F a(kg/s db). An electrical power E f(kW)is expended by the fan and a thermal power Q(kW)is expended by the heater.The air conditions for design can be consid-ered constant due to the high air recirculation.5.3.2P ROCESS M ODELA mathematical model of the process presented in Figure 5.4 is summ a rize d in Tabl e 5.10.Equation T10.1calculates the vapor pressure at drying temperature,whereas Equation T10.2is the psychrometric equation.Equation T10.1and Equa-tion T10.2are used to calculate the water activity at drying conditions(i.e.,temperature T and air humid-ity Y).Equation T10.3calculates the equilibrium material moisture content at drying conditions, whereas Equation T10.4estimates the drying time constant at drying conditions.Both Equation T10.3 and Equation T10.4are used in Equation T10.5, which calculates the required drying time.Equation T10.6and Equation T10.7constitute the moisture balance at the dryer.Equation T10.6 refers to solid,and Equation T10.7to air.The ther-mal energy requirements for drying aresummarized FIGURE5.4Schematic representation of a belt dryer.in Equat i on T10 .8 through Equation T10.11. Equa-tion T10 .8 refers to wat e r evap o ration, Equation T10.9 to solid s he a ting, Equat i on T10.10 to rejec t ed air heating , an d Equat i on T10.11 refer s to the total energy requir e d by the heater .Equat i on T10 .12 is used for sizing the heater . Equation T10 .13 throu g h Equation T10 .17 are used for sizi n g the belt.Equat i on T10 .13 correl a tes the reside n ce time with the mass hold u p, an d Equat i on T10.14 the mass hol d up with the vo l ume hold u p. These eq u a-tions are valid for all dryer types. Equation T10 .15 is the geomet r ical dist r ibution of the volume holdu p on the belt. Equation T10 .16 calcul a tes the required belt area, and Equat i on T10.17 the requir e d be l t veloci t y to obt a in the desired resi d ence time.Equat i on T10 .18 through Equat i on T10.20 are used for sizing the fan. Equat i on T10 .18 calcul a tes the pressure loss of air through the load e d belt. Equa-tion T10.19 co r relates the airﬂow with the air vel-ocity. Equation T10.20 esti m ates the requir e d electrica l power to ope r ate the fan.Equat i on T10.21 estimat e s the required electrica l power to mo v e the belt. Equat i on T10 .22 calcul a tes the req u ired total elect r ical power .Fin a lly, Equat i on T10.23 and Equation T10 .24 deﬁne two crucial dr y er perfor m ance indice s. Equa-tion T10 .23 deﬁnes the dryer thermal perfor m ance, whereas Equation T10 .24 calcul a tes the evap o rating capacity per unit belt area.Thi r ty-seven variables pr e sented in Tabl e 5.11 are involv e d in the model of 24 equatio n s present e d in Table 5.10. The corres p onding techn i cal data are summ a rized in Tabl e 5.12. The process speciﬁca t ions of a typical design prob l em are present e d in Table 5.13, wher e as a degrees -of-fre e dom an a lysis is sho w n in Table 5.14, whi c h results in four de s ign varia b les. Table 5.15 suggest s a selec t ion of de s ign v a riables and the corresp o nding solut i on algorithm is pr e sented in Table 5.16. The total an n ualiz e d cost (T A C) pr e-sented in Table 5.17 is used as object i ve function in process optim i zation. The requir e d cost data are summ a rized in Table 5.18.5.4 EXCEL IMPLEMENTATION OF A BELTDRYER DESIGNIn this sectio n the dryer design mo d el pr e sented in Sectio n 5.3 is implement e d in an Exc e l en v ironme n t accordi n g to the princi p les and techni q ues present e d in Se c tion 5.2.Steps 1–3 of Section 5.2 are applied and the dryer model is created on the spreadsheet ‘‘process’’ as shown in Figure 5.5. The ranges ‘‘Technical Data,’’ ‘‘Process Speciﬁcations,’’ ‘‘Design Variables,’’ and ‘‘Cost Data’’contain data according to Table 5.12, Table 5.13, Table 5.15, and Table 5.18, respectively. The range ‘‘Model Solution’’ contains the solution of the model in Table 5.10 according to the solution presented in Table 5.16, and the range ‘‘Cost Analysis’’ represents the analysis presented in Table 5.17. Finally, the button ‘‘optimize’’performs an optimization, i.e., it ﬁnds the (optimal) values of the design variables (Y, T, V, D), which min-imize the objective function (TAC). Figure 5.5 consti-tutes a simple but accurate belt dryer design simulator. Different problems (different material, ﬁnancial envir-onment, process speciﬁcations) can be solved instant-aneously.Step 4 of Section 5.2 is app l ied, as an exampl e, (a) to construct a dynamic process ﬂow sheet (Figure 5.6);TABLE 5.10Belt Dryer ModelPsychrometric equationsP s¼exp[a1Àa2/(a3þT)](T10.1) Y¼ma w P s/(PÀa w P s)(T10.2)Drying kineticsX e¼b1exp[b2/(273þT)][a w/(1Àa w)]b3(T10.3) t c¼c0d c1V c2T c3Y c4(T10.4) t¼Àt c ln[(XÀX e)/(X0ÀX e)](T10.5) Material balanceW¼F(X0ÀX)(T10.6) W¼F a(YÀY0)(T10.7) Thermal energy requirementsQ we¼F(X0ÀX)[D H0À(C PLÀC PV)T](T10.8) Q sh¼F[C PSþX0C PL](TÀT0)(T10.9) Q ah¼F a[C PAþY0C PV](TÀT0)(T10.10) Q¼Q weþQ shþQ ah(T10.11) Air heaterQ¼A s U s(T sÀT)(T10.12)Belt dryerM¼tF(1þX0)(T10.13) M¼(1À«)r s H(T10.14) H¼Z0DL(T10.15) A b¼LD(T10.16) u b¼L/t(T10.17)FanD P¼f1Z0V2(T10.18) F i¼r a VDL(T10.19)E f¼D PF f/r a(T10.20)Belt driverE b¼e1L(1þX0)F(T10.21)Electrical energy requirementsE¼E bþE f(T10.22)Performance indicesn¼Q we/Q(T10.23) r¼W/A b(T10.24)(b) to investiga t e the effe c t of one design variab l e on an eco n omic varia b le (Figur e 5.7); (c) to analyze the effect of two design varia b les on a techni c al varia b le (Figur e 5.8); (d) to summ a rize the resul t s of the de s ign on a syno p tic report (Figur e 5.9). Any other analys i sTABLE 5.11Process VariablesDrying air F a ton/h Fresh airﬂow rate F f ton/h Recycle airﬂow rate T 8CDrying air temperature Y kg/kg db Drying air humidity V m/s Drying air velocity P bar Drying pressureT 08CAmbient temperature Y 0kg/kg db Ambient humidityP s bar Vapor pressure at drying conditions a w —Water activity at drying conditions Material F ton/h Material ﬂow rateX 0kg/kg db Initial moisture content X kg/kg db Final moisture contentX e kg/kg db Equilibrium moisture content at drying conditions d m Particle sizet c h Drying time constant at drying conditions t h Drying timeDryer W ton/h Drying rate L m Dryer length D m Dryer widthM ton Dryer mass holdup H m 3Dryer volume holdup A b m 2Belt areaA s m 2Air heater transfer area u b m/s Belt velocity Z 0m Loading depthD PbarPressure loss of air ﬂowing through belt Thermal load Q we kW Water vaporization Q sh kW Solid heating Q ah kW Air heatingQ kW Total thermal load T s8C Steam temperature Electrical load E b kW Belt driver E f kW FanEkW Total power requirement Performance n —Thermal efﬁciencyrkg/h m 2Speciﬁc rate of evaporationTABLE 5.12Technical DataDensity (kg/m 3)r w Water r a Airr sDry material Speciﬁc heat (kJ/kg K)C PL WaterC PV Water vapor C PA AirC PSDry materialLatent heat (kJ/kg)D H 0Steam condensation at 08COther U s Heat transfer coefﬁcient at air heater (kW/m 2K)«Void (empty)fraction of loading Empirical constants a 1,a 2,a 3Antoine equation for vapor pressure of waterb 1,b 2,b 3Oswin equation for material isotherms c 0,c 1,c 2,c 3,c 4Drying kinetics equation e 1Belt driver power equation f 1Pressure loss equationTABLE 5.13Process SpeciﬁcationsF ton/h db Feed ﬂow rateX 0kg/kg db Initial material moisture content X kg/kg db Final material moisture content d m Material characteristic size T 08CAmbient temperature Y 0kg/kg db Ambient humidity Z 0m Loading depth P bar Ambient pressureT s8CHeating steam temperatureTABLE 5.14Degrees-of-Freedom AnalysisProcess variables 37Degrees of freedom 13Process equations 24Speciﬁcations 9Degrees of freedom13Design variables4TABLE 5.15Design VariablesY kg/kg db Drying air humidity T 8C Drying air temperature V m/s Drying air velocity DmBelt width。

OfficeWebComponents是什么？

What Are the Office Web Components?The Office Web Components are a set of Component Object Model (COM) controls designed to bring interactive spreadsheet modeling, database reporting, and data visualization to a number of control containers. The OWC library contains four principal components: Spreadsheet, Chart, PivotTable, and Data Source. We'll discuss each of these controls briefly in this section and in much more detail in the following chapters.NOTECOM is also known as ActiveX. I was on the Visual Basic team when Microsoft invented the term "ActiveX" to describe the COM technologies, throwing most of our customers for a loop since they had just gotten used to saying COM after we stopped using the term "OLE." Since I'm not a marketing person, I'll just use the term COM in this book to describe the Component Object Model technologies.The word "Office" in the name "Office Web Components" indicates that the controls were developed by some of the same programmers who created Microsoft Excel and Microsoft Access and that the controls were made to look, feel, and behave like small versions of their Microsoft Office siblings. These controls definitely don't have all the features found in Excel and Access—in other words, you wouldn't want to dynamically download all of Excel and Access to view a report in your browser! However, the controls do contain many of the commonly used features, especially those needed when interacting with content that's already been created. Plus, they can read and write the HTML file format of Excel 2000, allowing the user to click a button and load the current data into Excel for more powerful analysis. In this book, I'll detail the noteworthy Excel or Access features that are and aren't supported by each component. I'll also show you how to add some of these missing features with your own code.The "Web" part of OWC's name is often misleading. The controls are standard COM controls and can be used in many control containers such as Microsoft Internet Explorer, Microsoft Visual Basic, Microsoft Visual C++, Microsoft Visual FoxPro, or Microsoft Office UserForms. However, the controls have a few behaviors that make them especially suited to the unique environment of Internet Explorer. For example,web browsers automatically support scrolling along a document, and it's often annoying for a control in the page to have its own set of scroll bars. The Spreadsheet and PivotTable controls can be set to automatically adjust themselves to fit their current content without requiring internal scroll bars. Also, all the controls support the color names available in Internet Explorer in addition to supporting numeric RGB values. That means you can set the background color of an element to "CornSilk" or "PapayaWhip" (my personal favorite), and the control will convert the color to the appropriate RGB value just as Internet Explorer would.The "Components" part of OWC's name is a touch confusing, although it's more accurate than using the word "Controls" (though I will often refer to OWC as "controls" for convenience throughout this book). The Office Web Components are unusual in that they can be used in control containers like web pages, Visual Basic forms, and so on, as well as in memory as invisible objects. Most COM controls can be used only as visible controls in control containers, and most invisible objects, such as those accessed via the Microsoft ActiveX Data Objects (ADO) interface, can be used only in memory and cannot be put on a form or web page. The OWC library was built so that its components could be used either way, which enables you to use the controls with the user interfaces they expose or for their base services, such as spreadsheet recalculation. The ability to use the components as invisible objects also enables you to use the library on a server to easily generate static content that users can view in any web browser (more on that later in the chapter).All the controls support a rich set of programming interfaces that you can call from Microsoft VBScript (Visual Basic Scripting Edition), Microsoft JScript, Microsoft VBA (Visual Basic for Applications), Java, C++, and any other language capable of calling a dual or dispatch COM interface. That means you can weave the components into a custom solution and make them look and act the way you want. I will discuss most of the important properties, methods, and events in the subsequent chapters and will cover many more of these in the chapters describing the various solutions found on the companion CD.SEE ALSOIf you are looking for a definitive reference on COM, I'd recommend picking up a copy of David Chappell's Understanding ActiveX and OLE (Microsoft Press, 1996).Let's take a brief look at each of the components and discuss what kinds of solutions you can build with them. As already mentioned, the next four chapters will cover each component in more depth.The Spreadsheet ComponentThe Spreadsheet component (shown in Figure 1-1) is like a small version of an Excel spreadsheet, complete with a spreadsheet user interface and a recalculation engine that supports nearly all the calculation functions in Excel 2000. With this control, you can change or recalculate values; sort, filter, and scroll data; protect cells; and even reload the data into Excel 2000 for further manipulation. The Spreadsheet control can load its data from an embedded parameter or from any URL that points to an Excel spreadsheet saved in HTML file format.Figure 1-1.The Spreadsheet component.The Spreadsheet control is useful anytime you want to make a spreadsheet model available on your intranet so that others can change the input and instantly view the recalculated results. Examples include a mortgage calculator and payment schedule model, a product break-even model, and a sales forecasting model.This control is also useful for any kind of cross-tabulated or grid-based data entry, especially when you need to use formulas with automatic recalculation. Examples include expense reports, timesheets, and budgets.The Spreadsheet control has the ability to bind cells to properties of other objects on the page and then automatically update the cell and its dependents when the source indicates that the property value has changed. This makes it possible to feed real-time data into the spreadsheet for scenarios such as a stock portfolio.The Spreadsheet control is specifically designed to keep listening for new values and recalculating even when you are editing other formulas or formatting other cells in the spreadsheet you're working on.The Chart ComponentThe Chart component (shown in Figure 1-2) is comparable to a small version of Excel charting, supporting most of the two-dimensional chart types in Excel 2000 as well as a Polar chart type. Another big feature is that the Chart control can display many plots at once, allowing you to create a small-multiple design—in other words, a collection of plots that vary by one property and can be compared at a glance. A chart can be data-bound to the Spreadsheet control, the PivotTable control, or an ADO Recordset object, or it can be filled with literal data values. When bound to a data source, a Chart control will update whenever the source data changes.SEE ALSOFor more information on the power of small-multiple designs, see Edward Tufte's book Envisioning Information (Graphics Press, 1990).Figure 1-2.The Chart component.The Chart control is primarily useful any time you need to chart live data or monitor a specific metric critical to your business. Because it supports a rich programming model, you can also add many effects to a chart with this control, such as zooming and panning on large axes, dynamically changing other content in the application based on the mouse's location, or letting users double-click to link to a new page displaying more information about the selected data point.The PivotTable ComponentDesigned to deliver interactive data reporting and analysis, the PivotTable component (shown in Figure 1-3) provides all the functionality found in Excel PivotTables and external data ranges. It can retrieve data from tabular, relational databases through OLE DB, as well as from OLAP server cubes and cube files through OLE DB for OLAP. Using this control, you can view data grouped, sliced, and sorted in a variety of ways, creating polished reports and interactive analysis on live data.You can use this control for many tasks, although it's best suited for database reporting and data analysis solutions. When bound to an OLAP cube, the PivotTable control can provide the user with a flexible, high-performing analysis surface. IT groups can concentrate on collecting and cleaning data and loading it into cubes thatreflect the way their company thinks about the data, while users working with this control can create slices of the data to fit their own needs.Figure 1-3.The PivotTable component.The PivotTable control can also perform the same operations directly on a relational database, so you can use it even if you don't have an investment in an OLAP system. However, the performance when using an OLAP data source is always much faster because of the nature of the technology. OLAP has other logical benefits that we'll discuss further when we explore the Sales Analysis and Reporting solution in Chapter 7.The Data Source ComponentThe Data Source component (DSC) is the backbone for controls that require data from external sources. Although this control is invisible, it is widely used to retrieve data, manipulate data into hierarchies or temporary OLAP cubes (more on this in Chapter 4), and establish data bindings between the various controls. Since the DSC supports the same standard interfaces as other data source controls found in Internet Explorer and Visual Basic, it will interoperate in those environments. The DSC is used heavily in Access 2000's data access pages feature and encapsulates much of the functionality found in the Access reporting engine.The DSC is involved almost any time the other components retrieve data from an external database. However, it also supports a programming model of its own, and you can use it to build or manipulate hierarchical Recordset objects. In general, you don't need to think much about the DSC since the other components and the Access 2000 Data Access Page Designer will set it up and implement it for you.Office Web Components是什么？Office Web Components是一组的COM控件，设计的目的是为众多的控件容器提供交互的电子表格建模，数据报表和数据可视化功能。

制药行业过程自动化及法规遵从

Signatures Spreadsheet Validation Business Systems Validation
Facility and Equipment Validation Education and Training Validation Outsourcing
© ABB Life Sciences - 3
Definition:
Validation is establishing documented evidence which provides a high degree of assurance that a specific process will consistently produce a product meeting its predetermined specifications and quality attributes.
挑战
市场变化和技术更新
如何平衡产业不断发生的变化并在应用新技术的同时满足遵从规范解决方案的要求
时间和资源的短缺
如何利用有限的时间和资源，以保持与规范发展同步，始终做好被检查的准备
一定的质量产品和好的价格
如何在严峻的经济条件下满足客户对于质量优质,价格适宜标准的要求
验证的目的
© ABB Life Sciences - 14
Computer Infrastructure Qualification
计算机的基础架构 :
服务器上存储有数据、数据库、各种文件、应用或者特殊服务 ,客户工作站 ,网络组件和协议
负责各种资源间的协调并将其分配给相应的用户和应用，以进行数据共享提供通讯服务
Risk Analysis
•Specify functional requirements

ISPE新指南：数据完整性--关键概念201810

ISPE新指南：数据完整性--关键概念201810 ISPE推出新指南：GAMP RDI Good Practice Guide: Data Integrity - Key ConceptsGAMP RDI优良规范指南：数据完整性--关键概念先上官⽅图⼀张对，你没看错，就是这么贵------会员价160美⼑=133欧，⾮会员价350美⼑=292欧，当然，还有特殊地区价格，不过作为⾃豪的中国⼈，我们好像不属于。

我知道你⼀定是下⾯这个样⼦为了勾引⼤家买，官⽅⾃然是要⼀如往常地放出TOC（⽬录）来让⼤家蓝瘦⾹菇⼀下了，官⽅TOC的PDF下载链接如下哈https:///sites/default/files/publications/manuals/GAMP_RDIGPG1-DICON_TOC.pdf ISPE⼤概是想说具体介绍如下Published:October 2018Pages: 196Bound version ships after 26 October 2018The ISPE GAMP® RDI Good Practice Guide: Data Integrity – Key Concepts provides detailed practical guidance to support dataintegrity within a regulated organization.In recent years significant problems with data integrity have been found in the pharmaceutical, biotechnology, and medical device industries worldwide. This ultimately affects patients, as patient safety is intrinsically impacted by the integrity and quality of the data on which aregulatory decision is based.Additionally, the implementation of behavioral, procedural, and technical solutions to meet regulatory requirements throughout the business process proves to be challenging for organizations that do not have expertise in incorporating data integrity into their daily activities. This Guide integrates tools such as Cultural Excellenceand critical thinking skills into data integrity practices to aid companies in meeting regulatory requirements and expectations. Numerous examples of good data integrity practices along with ways to identify risks anddetect issues are included to assist organizations in developing or raising their data integrity awareness.This Guide is positioned under the ISPE GAMP®Guide: Records and Data Integrity and is aligned with ISPE GAMP® 5:A Risk-Based Approach to Compliant GxP Computerized Systems.出版⽇期：2018年10⽉页数：196该指南为受法规管理的组织内的数据完整性提供详细的实践指南⽀持。

IPC目录大全

IPC目录大全一、设计（Design）部分IPC-M-106 Technology Reference for Design Manual 设计技术手册IPC-2220 Design Standard Series 设计标准系列手册IPC-2221A Generic Standard on Printed Board Design 印制板设计通用标准IPC-2222 Sectional Standard on Rigid Organic Printed Boards刚性有机印制板设计分标准IPC-2223 Sectional Design Standard for Flexible Printed Boards挠性印制板设计分标准IPC-2224 Sectional Standard of Design of PWB for PC Card PC卡用印制电路板分设计分标准IPC-2225 Sectional Design Standard for Organic Multichip Modules (MCM-L) and MCM-L Assemblies 有机多芯片模块(MCM-L)及其组装件设计分标准IPC-2226 Sectional Design Standard for High Density Interconnect (HDI) Printed Boards高密度互连(HDI)印制板设计分标准IPC-SM-782A Surface Mount Design and Land Pattern Standard--Includes Amendments 1 & 2 表面安装设计及连接盘图形标准(包括修订1和2)IPC-EM-782 Surface Mount Design & Land Pattern Standard Spreadsheet表面安装设计及连接盘图形标准IPC-D-859 Design Standard for Thick Film Multilayer Hybrid Circuits厚膜多层混合电路设计标准IPC-1902 IPC/IEC Grid Systems for Printed Circuits IPC/IEC印制电路网格体系SMC-WP-004 Design for Success 成功的综合设计分析手册IPC-PWB-EVAL-CH Printed Circuit Board Defect Evaluation Chart 印制板缺陷评估图册IPC/JPCA-2315 Design Guide for High Density Interconnects & Microvias高密度互连(HDI)和微通孔设计指南IPC-2615 Printed Board Dimensions and Tolerances 印制板尺寸和公差IPC-A-311 Process Controls for Phototool Generation and Use照相版制作和使用的过程控制IPC-D-279 Design Guidelines for Reliable Surface Mount Technology Printed Board Assemblies 高可靠表面安装印制板组装件技术设计导则IPC-D-310C Guidelines for Phototool Generation and Measurement Techniques照相版制作指南和测量技术IPC-D-322 Guidelines for Selecting Printed Wiring Board Sizes Using Standard Panel Sizes使用标准在制板尺寸的印制板尺寸选择指南IPC-D-422 Design Guide for Press Fit Rigid Printed Board Back Plane压配合刚性印制背板设计指南IPC-PWBADV-SG02 (HARD COPY)IPC-PWB ADV-CD (CD) PCB Advanced Designer Certification Study Guide印制电路板高级设计师证书学习指南和多媒体光盘IPC-PWB-CRT-SG01 (HARD COPY)IPC-PWB-CERTCD1 (CD) PCB Designer Certification Study Guide 印制电路板设计师证书学习指南和多媒体光盘IPC-2531 Standard Recipe File Format SpecificationSMEMA发布：标准“菜单”（过程控制）文件格式规范注：SMEMA{The Surface Mount Equipment Manufacturers Association merged with IPC}IPC-2541 Generic Requirements for Electronics Manufacturing Shop Floor Equipment Communication电子制造车间现场设备信息沟通(CAMX)通用要求IPC-2546 Sectional Requirements for Specific Printed Circuit Board Assembly Equipment特殊印制板组装设备分要求IPC-2547 Sectional Requirements for Shop Floor Electronic Inspection and Test Equipment Communication 车间现场电子检验及测试设备信息沟通分要求IPC-2571 Generic Requirements for Electronics Manufacturing Supply Chain Communication - Product Data eXchange (PDX) 电子制造供应链信息沟通分要求产品数据交换IPC-2576 Sectional Requirements for Electronics Manufacturing Supply Chain Communication of As-Built Product Data – Product Data eXchange 制成态产品-产品数据电子制造供应链信息沟通分要求IPC-2578 Sectional Requirements for Supply Chain Communication of Bill of Material and Product Design Configuration Data-Product Data eXchange 材料单及产品设计构造数据-产品数据交换供应链信息沟通分要求IPC-2511A Generic Requirements for Implementation of Product Manufacturing Description Data & Transfer Methodology 实施产品制造数据描述及其传输方法学的通用要求IPC-2501 Definition for Web-Based Exchange of XML Data XML数据网络交换定义IPC-2511B Generic Requirements for Implementation of Product Manufacturing Description Data & Transfer XML Schema Methodology实施产品制造数据描述及其网络传输方法学的通用要求IPC-2512A Sectional Requirements for Implementation of Administrative Methods for Manufacturing Data Description 实施制造数据描述管理方法的分要求IPC-2513A Sectional Requirements for Implementation of Drawing Methods for Manufacturing Data Description 实施制造数据描述绘制方法的分要求IPC-2514A Sectional Requirements for Implementation of Printed Board Manufacturing Data Description 实施印制板制造数据描述的分要求IPC-2515A Sectional Requirements for Implementation of Bare-Board Product Testing Data Description 实施裸板成品测试数据描述的分要求IPC-2516A Sectional Requirements for Implementation of Assembled Board Product Manufacturing Data Description 实施已组装板制造数据描述的分要求IPC-2517A Sectional Requirements for Implementation of Assembly In-Circuit Test Data Description 实施组装件在线测试数据描述的分要求IPC-2518A Sectional Requirements for Implementation of Parts List Product Manufacturing Data Description 实施零部件制造数据描述的分要求IPC-D-356B Bare Board Electrical Test Data Format 裸基板电检测的数据格式二、印制电路板（Printed Circuit Boards）IPC-M-105 Rigid Printed Board Manual 刚性印制板设计手册IPC-D-325A Documentation Requirements for Printed Boards 印制板设计文件图册要求IPC-PE-740A Troubleshooting for Printed Board Manufacture and Assembly印制板制造和组装的故障排除IPC-6010 Series IPC-6010 Qualification and Performance SeriesIPC-6010印制电路板质量标准和性能规范系列手册IPC-6011 Generic Performance Specification for Printed Boards 印制板通用性能规范IPC-6013-K Qualification & Performance Specification for Flexible Printed Boards (Includes Amendment 1) 挠性印制板的鉴定与性能规范（包括修改单1）IPC-6016 Qualification & Performance Specification for High Density Interconnect(HDI) Layers or Boards 高密度互连(HDI)层或印制板的鉴定与性能规范IPC-6012A-AM Qualification and Performance Specification for Rigid Printed Boards, Includes Amendment 1 刚性印制板的鉴定与性能规范 (包括修改单1)IPC-6018A Microwave End Product Board Inspection and Tech 微波成品印制板的检验和测试IPC-6015 Qualification & Performance Specification for Organic Multichip Module (MCM-L) Mounting and Interconnections 有机多芯片模块(MCM-L)安装及互连结构的鉴定与性能规范IPC-A-600F Acceptability of Printed Boards 印制板验收条件IPC-QE-605A Printed Board Quality Evaluation Handbook 印制板质量评价IPC-QE-605A-KIT Hard Copy and CD 印制板质量评价书和光盘(CD)IPC-HM-860 Specification for Multilayer Hybrid Circuits多层混合电路规范IPC-TF-870 Qualification and Performance of Polymer Thick Film Printed Boards聚合物厚膜印制板的鉴定与性能IPC-ML-960 Qualification and Performance Specification for Mass Lamination Panels for Multilayer printed Boards 多层印制板的鉴定与性能规范用预制内层在制板的鉴定与性能规范IPC-TR-481 Results of Multilayer Tests Program Round Robin多层印制板联合试验计划结果IPC-TR-551 Quality Assessment of Printed Boards Used for Mounting and Interconnecting Electronic Components 用于电子元件安装与互连的印制板质量评价IPC-TR-579 Round Robin Reliability Evaluation of Small Diameter Plated Through Holes in PCBs 印制板中小直径镀覆孔可靠性评价联合试验IPC-4552 Specification for Electroless Nickel/Immersion Gold(ENIG) Plating for Printed Circuit Boards 印制电路板表面非电镀镍/沉金规范IPC-DR-572 Drilling Guidelines for Printed Boards 印制板钻孔导则IT-95080 Improvements/Alternatives to Mechanical Drilling of PCB Vias印制板通孔机加工方案的改进和优选手册IPC-NC-349 Computer Numerical Control Formatting for Drillers and Routers钻床和铣床用计算机数字控制格式IPC-SM-839 Pre & Post Solder Mask Application Cleaning Guidelines施加阻焊前及施加后清洗导则IPC-HDI-1 High Density Interconnect Microvia Technology Compendium高密度(HDI)互连微通孔技术纲要IPC/JPCA-4104 Specification for High Density Interconnect (HDI) and Microvia Materials高密度互连(HDI)及微导通孔材料规范IPC-6016 Qualification & Performance Specification for High Density Interconnect (HDI) Layers or Boards 高密度互连(HDI)层或印制板的鉴定与性能规范IPC/JPCA-6801 IPC/JPCA Terms & Definitions, Test Methods, and Design Examples for Build-Up/High Density Interconnection 积层/高密度互连的术语和定义、试验方法与设计例IPC-DD-135 Qualification Testing for Deposited Organic Interlayer Dielectric Materials for Multichip Modules 多芯片组件内层有机绝缘材料的鉴定试验IT-96060 High Density PCB Microvia Evaluation (October Project), Phase I, Round 1高密度印制板微通孔评价指标手册, 第一期第一版IT-97071 High Density PCB Microvia Evaluation, Phase I, Round 2高密度印制板微通孔评价指标手册, 第一期第二版IT-30101 High Density PCB Microvia Evaluation, Phase I, Round 3高密度印制板微通孔评价指标手册, 第一期第三版IT-98123 Microvia Manufacturing Technology Cost Analysis Report微通孔制作技术成本核算报告IPC-2141 Controlled Impedance Circuit Boards & High Speed Logic Design控制阻抗电路板与高速逻辑设计IPC-2252 Design Guide for RF/Microwave Circuit Boards 射频/微波电路板设计指南IPC-4103 Specification for Base Materials for High Speed/High Frequency Applications 高速高频用基材规范IPC-6018A Microwave End Product Board Inspection and Test 微波成品印制板的检验和测试IPC-D-317A Design Guidelines for Electronic Packaging Utilizing High Speed Techniques采用高速技术电子封装设计导则IPC-M-102 Flexible Circuits Compendium 挠性电路纲要IPC-4202 Flexible Base Dielectrics for Use in Flexible Printed Circuitry挠性印制线路用挠性绝缘基底材料IPC-4203 Adhesive Coated Dielectric Films for Use as Cover Sheets for Flexible Printed Circuitry and Flexible Adhesive Bonding Films 挠性印制线路覆盖层用涂粘接剂绝缘薄膜IPC-4204 Flexible Metal-Clad Dielectrics for Use in Fabrication of Flexible Printed Circuitry挠性金属箔去电应用于柔性电路组装IPC-6013-K Qualification & Performance Specification for Flexible Printed Boards & Amendment 1 挠性印制板的鉴定与性能规范（包括修改单1）IPC/JPCA-6202 IPC/JPCA Performance Guide Manual for Single- and Double-Sided Flexible Printed Wiring Boards IPC/JPCA单双面挠性印制板性能手册IPC-FA-251 Guidelines for Assembly of Single- and Double-Sided Flex Circuits单面和双面挠性电路组装导则IPC-FC-234 Composite Metallic Materials Specification for Printed Wiring Boards印制线路板复合金属材料规范IPC-MB-380 Guidelines for Molded Interconnection Devices 模压互连器件导则IPC-M-107 Standards for Printed Board Materials Manual 印制板材料标准手册IPC-MI-660 Incoming Inspection of Raw Materials Manual 原材料接收检验手册IPC-4101A Specifications for Base Materials for Rigid and Multilayer Printed Boards刚性及多层印制板用基材规范IPC-4121 Guidelines for Selecting Core Construction for Multilayer Printed Wiring Board Applications 多层印制板用芯板结构选择导则IPC-4562 Metal Foil for Printed Wiring Applications 印制线路用金属箔IPC-CF-148A Resin Coated Metal for Printed Boards 印制板用涂树脂金属箔IPC-CF-152B Composite Metallic Materials Specification for Printed Wiring Boards印制线路板复合金属材料规范IPC-TR-482 New Developments in Thin Copper Foils 薄铜箔的新发展IPC-TR-484 Results of IPC Copper Foil Ductility Round Robin StudyIPC铜箔延展性联合研究结果IPC-TR-485 Results of Copper Foil Rupture Strength Test Round Robin Study铜箔断裂强度试验联合研究结果IPC-4412 Specification for Finished Fabric Woven from ”E” Glass for Printed Boards“E”类精纺玻璃纤维层印制板技术规范IPC-4130 Specification & Characterization Methods for Nonwoven "E" Glass MaterialsE 玻璃纤维非织布材料规范及性能确定方法IPC-4110 Specification and Characterization Methods for Nonwoven Cellulose Based Paper for Printed Boards印制板用纤维纸规范及性能确定方法IPC-4411-K Specification and Characterization Methods for Non-Woven Para-Aramid Reinforcement, with Amendment 1 聚芳基酰胺非织布规范及性能确定方法, 包括修改单 1IPC-4411-AM1 Specification and Characterization Methods for Non-Woven Para-Aramid Reinforcement, Amendment 1 关于聚芳基酰胺非织布规范及性能确定方法的修改单 1IPC-SG-141 Specification for Finished Fabric Woven from "S" Glass for Printed Boards印制板用经处理S玻璃纤维织物规范IPC-A-142 Specification for Finished Fabric Woven from Aramid for Printed Boards印制板用经处理聚芳酰胺纤维编织物规范IPC-QF-143 Specification for Finished Fabric Woven from Quartz (Pure Fused Silica) for Printed Boards 印制板用经处理石英（熔融纯氧化硅）纤维编织物规范IPC-2524 PWB Fabrication Data Quality Rating System 印制板制造数据质量定级体系IPC-9151A Printed Board Process, Capability, Quality and Relative Reliability Benchmark Test Standard and Database印制板工艺, 容量, 质量,可靠性试验标准和数据库IPC-9191 General Guidelines for Implementation of Statistical Process Control (SPC) 实施统计过程控制(SPC)的通用导则IPC-9199 Statistical Process Control (SPC) Quality Rating 统计分析控制IPC-9252 Guidelines and Requirements for Electrical Testing of Unpopulated Printed Boards 未组装印制板电测试要求和指南IT-97061 PWB Hole to Land Misregistration: Causes and Reliability印制线路板通孔与焊盘的错位: 原因和可靠性IT-98103 Reliability of Misregistered and Landless Innerlayer Interconnects in Thick Panels 多层板内部无焊盘层互连错位的可靠性IPC-MS-810 Guidelines for High V olume Microsection 大批量显微剖切导则IPC-QL-653A Certification of Facilities that Inspect/Test Printed Boards, Components &Materials 印制板、元器件及材料检验试验设备的认证IPC-TR-483 Dimensional Stability Testing of Thin Laminates-Report on Phase 1 & 2 International Round Robin Test薄层压板尺寸稳走性试----国际联合试验计划I阶段及II阶段报告IPC-TR-486 Round Robin Study to Correlate IST & Microsectioning Evaluations for Inner-Layer Separation 内层分离的互连应力测试(IST)与显微剖切相关性联合研究三、电子组装（Assembly）IPC-T-50F Terms and Definition for Interconnecting and Packaging Electronic Circuits电子电路互连与封装的定义和术语IPC-S-100 Standards and Specifications Manual标准和详细说明汇编手册IPC-E-500 IPC Electronic Document Collection已出版的IPC标准电子文档资料合订本IPC-TM-650 Test Methods Manual试验方法手册IPC-ESD-20-20 Association Standard for the Development of an ESD Control Program静电释放控制过程(由静电释放协会制定)IPC/EIA J-STD-001C Requirements for Soldered Electrical & Electronic Assemblies电气与电子组装件锡焊要求IPC-HDBK-001 Handbook and Guide to Supplement J-STD-001—Includes Amendment 1J-STD-001辅助手册及指南及修改说明1IPC-A-610C Acceptability of Electronic Assemblies印制板组装件验收条件IPC-HDBK-610 Handbook and Guide to IPC-A-610 (Includes IPC-A-610B to C ComparisonIPC-610手册和指南(包括IPC-A-610B和C的对比)IPC-EA-100-K Electronic Assembly Reference Set电子组装成套手册，包括：IPC/EIA J-STD-001C，IPC-HDBK-001，IPC-A-610C。

关于电脑软件英语作文

关于电脑软件英语作文在本次作文中，我将以一篇网上下载量最高的电脑软件英语作文为参考，并根据原文进行高质量的仿写。

下面是原文：---。

Title: The Importance of Computer Software。

In today's digital age, computer software plays a crucial role in almost every aspect of our lives. From personal use to business operations, the significance of software cannot be overstated.Firstly, computer software enhances productivity and efficiency. With the right software tools, tasks that used to take hours can now be completed within minutes. For example, office suites like Microsoft Office streamline document creation, spreadsheet management, and presentation design, enabling workers to accomplish more in less time. This increased efficiency translates to cost savings andimproved competitiveness for businesses.Secondly, computer software facilitates communication and collaboration. Email clients, instant messaging apps, and video conferencing software enable seamless communication between individuals and teams regardless of geographical location. This is especially vital in today's globalized world where remote work is becoming increasingly common. Moreover, collaborative tools such as Google Drive and Dropbox allow multiple users to work on the same documents simultaneously, fostering teamwork and innovation.Furthermore, computer software drives innovation and creativity. From graphic design software like Adobe Photoshop to music production software like Ableton Live, creative professionals rely on specialized tools to bring their ideas to life. These software applications not only provide advanced features and functionalities but also empower users to experiment and push the boundaries oftheir creativity.Additionally, computer software plays a pivotal role ineducation and skill development. Educational software, such as interactive learning platforms and simulation tools, enhances the learning experience by making complex concepts more engaging and accessible. Furthermore, programming environments like Scratch and Python enable students to develop computational thinking and coding skills from an early age, preparing them for future careers in technology.In conclusion, computer software is indispensable in today's interconnected world. Its role in enhancing productivity, facilitating communication and collaboration, driving innovation, and supporting education cannot be ignored. As technology continues to evolve, the importance of computer software will only grow, shaping the way we live, work, and interact with the world around us.---。

Chapter06-运输问题和指派问题

Copyright 2007 © 深圳大学管理学院运筹学 19
The P&T Co. Transportation Problem
运输问题模型参数表(供应量、需求量和单位成本)
Copyright 2007 © 深圳大学管理学院运筹学 20
Spreadsheet Formulation
Copyright 2007 © 深圳大学管理学院运筹学 21
Copyright 2007 © 深圳大学管理学院运筹学 5
P&T Company Distribution Problem
CANNERY 1 Bellingham
罐头厂1-贝林翰
CANNERY 2 Eugene
罐头厂2-尤基尼
WAREHOUSE 3 Rapid City
仓库3-赖皮特城
CANNERY 3 Albert Lea
Copyright 2007 © 深圳大学管理学院运筹学 2
Table of Contents (主要内容)
Variants of Transportation Problems: Nifty (Section 6.3)(运输问题的变形：耐芙迪公司问题) Applications of Transportation Problems: Metro Water (Section 6.4)(运输问题的应用：米德罗水管站问题) Applications of Transportation Problems: Northern Airplane (Section 6.4)(运输问题的应用：北方飞机制造公司问题)
贝林翰先满足萨克拉门托，剩余的运送到盐湖城艾尔贝先满足奥尔巴古，剩余的运送到赖皮特尤基尼满足剩余需求

Spreadsheet Modeling & Decision Analysis

13-3
The Purpose of Queuing Models
• Queuing models are used to:
– describe the behavior of queuing systems – determine the level of service to provide – evaluate alternate configurations for providing service
• It is estimated that Americans spend a total of 37 billion hours a year waiting in lines. • Places we wait in line... ▪ stores ▪ hotels ▪ post offices ▪ banks ▪ traffic lights ▪ restaurants ▪ airports ▪ theme parks ▪ on the phone • Waiting lines do not always contain people... ▪ returned videos ▪ subassemblies in a manufacturing plant ▪ electronic message on the Internet • Queuing theory deals with the analysis and management of waiting lines.
• Arrival rate - the manner in which customers arrive at the system for service. • Arrivals are often described by a Poisson random variable:

数据、模型与决策(运筹学)课后习题和案例答案003

CHAPTER 3 THE ART OF MODELING WITH SPREADSHEETSReview Questions3.1-1 The long-term loan has a lower interest rate.3.1-2 The short-term loan is more flexible. They can borrow the money only in the yearsthey need it.3.1-3 End with as large a cash balance as possible at the end of the ten years after payingoff all the loans.3.2-1 Visualize where you want to finish. What should the “answer” look like?3.2-2 First, it can help clarify what formula should be entered for an output cell. Second,hand calculations help to verify the spreadsheet model.3.2-3 Sketch a layout of the spreadsheet.3.2-4 Try numbers in the changing cells for which you know what the values of the outputcells should be.3.2-5 Relative references are based upon the position relative to the cell containing theformula. Absolute references refer to a specific cell address.3.3-1 Enter the data first.3.3-2 Numbers should be entered separately from formulas in data cells.3.3-3 With range names, the formulas and Solver dialogue box contain descriptive rangenames rather than obscure cell references. Use a range name that corresponds exactly to the label on the spreadsheet.3.3-4 Borders, shading, and colors can be used to distinguish data cells, changing cells,output cells, and target cells on a spreadsheet.3.3-5 Three. One for the left-hand-side, one for the inequality sign, and one for the right-hand-side.3.4-1 Try different values for the changing cells for which you can predict the correct resultin the output cells and see if they calculate as expected.3.4-2 Control-~ on a PC (command-~ on a Mac).3.4-3 The auditing tools can be used to trace dependents or precedents for a given cell.Problems3.13.2a. The COO will need to know how many of each product to produce. Thus, the decisions are how many end tables, how many coffee tables, and how many dining room tables to produce. The objective is to maximize total profit.b. Pine wood used = (3 end tables)(8 pounds/end table)+ (3 dining room tables)(80 pounds/dining room table)= 264 pounds Labor used = (3 end tables)(1 hour/end table) + (3 dining room tables)(4 hours/dining room table) = 15 hoursc.E nd TablesCoffee TablesDining Room TablesUnit P rofitAvailableP ine Wood<=<=Units P roducedd.3.3a. Top management will need to know how much to produce in each quarter. Thus,the decisions are the production levels in quarters 1, 2, 3, and 4. The objective is to maximize the net profit.b. Ending inventory(Q1)= Starting Inventory(Q1) + Production(Q1) – Sales(Q1)= 1,000 + 5,000 – 3,000 = 3,000 Ending inventory(Q2) = Starting Inventory(Q2) + Production(Q2) – Sales(Q2)= 3,000 + 5,000 – 4,000 = 4,000 Profit from sales(Q1) = Sales(Q1) * ($20) = (3,000)($20) = $60,000 Profit from sales(Q2) = Sales(Q2) * ($20) = (4,000)($20) = $80,000 Inventory Cost(Q1) = Ending Inventory(Q1) * ($8) = (3,000)($8) = $24,000 Inventory Cost(Q2) = Ending Inventory(Q2) * ($8) = (4,000)($8) = $32,000c.Inventory Holding C ost Gross P rofit from SalesStarting M axim um Dem and/E nding Inventory Gross ProfitNet P rofitd.e.3.4a. Fairwinds needs to know how much to participate in each of the three projects, and what their ending balances will be. The decisions to be made are how much to participate in each of the three projects. The objective is to maximize the ending balance at the end of the 6 years.b. Ending Balance(Y1) = Starting Balance + Project A + Project C + Other Projects = 10 + (100%)(–4) + (50%)(–10) + 6= 7 (in $millions) Ending Balance(Y2) = Starting Balance + Project A + Project C + Other Projects = 7 + (100%)(–6) + (50%)(–7) + 6 = 3.5 (in $millions)c.Starting C ashTotalCash Flow (at full participation, $m illion)Cash Flow OtherE nding M inim um Year123456P articipationd.e.3.5a. Web Mercantile needs to know each month how many square feet to lease andfor how long. The decisions therefore are for each month how many square feet to lease for one month, for two months, for three months, etc. The objective is to minimize the overall leasing cost.b. Total Cost = (30,000 squarefeet)($190 per square foot) + (20,000 square feet)($100 per square foot)= $7.7 million.c.M onth Covered by Lease?Total Space M onth of Lease:111112222333445Leased Required Length of Lease:M onth 1M onth 2M onth 3M onth 4M onth 5Cost of Lease (per sq. ft.)Lease (sq. ft.)d.e.3.6a. Larry needs to know how many employees should work each possible shift. Therefore, the decision variables are the number of employees that work each shift. The objective is to minimize the total cost of the employees.b. Working 8am-noon: 3 FT morning + 3 PT = 6 Working noon-4pm: 3 FT morning + 2 FT afternoon + 3 PT = 8 Working 4pm-8pm: 2 FT afternoon + 4 FT evening + 3 PT = 9 Working 8pm-midning: 4 FT evening + 3 PT = 7 Total cost per day = (3+2+4 FT)(8 hours)($14/hour) + (12 PT)(4 hours)($12/hour) = $1,584.c.Full Tim eFull Tim e Full Tim e P art Tim e P art Tim e P art Tim e P art Tim e Total Total 8am 4pm 8pm -m idnight Total Total Tim e of Day 8am 4pm 8pm -m idnightd.3.7a. Al will need to know how much to invest in each possible investment each year.Thus, the decisions are how much to invest in investment A in year 1, 2, 3, and 4; how much to invest in B in year 1, 2, and 3; how much to invest in C in year 2; and how much to invest in D in year 5. The objective is to accumulate the maximum amount of money by the beginning of year 6.b. Ending Cash (Y1) = $60,000 (Starting Balance) – $20,000 (A in Y1) = $40,000Ending Cash (Y2) = $40,000 (Starting Balance) – $20,000 (B in Y2) – $20,000 (C in Y2) = $0 Ending Cash (Y3) = $0 (Starting Balance) + $20,000(1.4) (for investment A) = $28,000 Ending Cash (Y4) = $28,000 (Starting Balance) Ending Cash (Y5) = $28,000 (Starting Balance) + $20,000(1.7) (investment B) = $62,000 Ending Cash (Y6) = $62,000 (Starting Balance) + $20,000(1.9) (investment C) = $100,000c.Beginning BalanceM inim um BalanceInvestm entA A A AB B BCDE nding Minimum >=>=>=>=>=>=Dollars Investedd.e.3.8 In the poor formulation, the data are not separated from the formula—they areburied inside the equations in column C. In contrast, the spreadsheet in Figure 3.6 separates all of the data in their own cells, and then the formulas for hours used and total profit refer to these data cells.In the poor formulation, no range names are used. The spreadsheet in Figure 3.6 uses range names for UnitProfit, HoursUsed, TotalProfit, etc.The poor formulation uses no borders, shading, or colors to distinguish between cell types. The spreadsheet in Figure 3.6 uses borders and shading to distinguish the data cells, changing cells, and target cell.The poor formulation does not show the entire model on the spreadsheet. There is no indication of the constraints on the spreadsheet (they are only displayed in the Solver dialogue box). Furthermore, the right-hand-sides of the constraints are not on the spreadsheet, but buried in the Solver dialogue box. The spreadsheet in Figure 3.6 shows all of the constraints of the model in three adjacent cells on the spreadsheet.3.9 Cell F16 has –0.47 for LT Interest, rather than –LTRate*LTLoan.Cell G14 for the 2006 ST Interest uses the LT Loan amount rather than the ST Loan amount.Cell H21 for LT Payback refers to the 2006 ST Loan rather than the LT Loan to determine the payback amount.3.10 Cell G21 for the 2013 ST Interest uses LTRate instead of STRate.Cell H21 for LT Payback in 2013 as –6.649 instead of –LTLoan.Cell I15 for ST Payback in 2007 has –LTLoan instead of –E14 (LT Loan for 2006). Case3.1 a. PFS needs to know how many units of each of the four bonds to purchase, howmuch to invest in the money market, and their ending balance in the moneymarket fund each year after paying the pensions. The decisions are how manyunits of each bond to purchase, as well as the initial investment in 2003 in themoney market. The objective is to minimize the overall initial investment necessaryin 2003 in order to meet the pension payments through 2012.b. Payment received from Bond 1 (2004) = (10 thousand units) ($1,000 face value) +(10,000 units) ($1,000 face value) (0.04 coupon rate) = $10.4 million Payment received from Bond 1 (2005) = $0Payment received from Bond 2 (2004) = (10 thousand units) ($1,000 face value)(0.02 coupon) = $0.2 millionPayment received from Bond 2 (2005) = (10 thousand units) ($1,000 face value)(0.02 coupon) = $0.2 millionBalance in money market fund (2003) = $28 million (initial investment)–$8 million (pension payment)= $20 millionBalance in money market fund (2004) = $20 million (starting balance)+ $10.4 million (payment from Bond 1)+ $0.2 million (payment from Bond 2)–$12 million (pension payment)+ $1 million (money market interest)= $19.6 millionBalance in money market fund (2005) = $19.6 million (starting balance)+ $0.2 million (payment from Bond 2)–$13 million (pension payment)+ $0.98 million (money market interest)= $7.78 millionc. PFS will need to track the flow of cash from bond investments, the initialinvestment, the required pension payments, interest from the money market, and the money market balance. The decisions are the number of units to purchase of each bond. Data for the problem include the yearly cash flows from the bonds (per unit purchased), the money market rate, and the minimum required balance in the money market fund at the end of each year. A sketch of a spreadsheet model might appear as follows.3-11Money Market RateMinimum Required BalanceRequired Money Money Bond Initial P ension Market Market20030200402005020060200702008020090201002011020120Units P urchasedBond Cash Flow s (per unit)。

运筹学作业d 文档

注：没有选项的题是判断题，每一章的前几道都是判断题Chapter 11. Managers do not need to know the mathematical theory behind the techniques of management science in order to lead management science teams.2. Management scientists are responsible for making the managerial decisions for an organization.3. Once management makes its decisions, the management science team typically continues to work to implement the new plan.4. At the break-even point, the fixed cost equals the variable cost.5. Sensitivity analysis is used to check the effect on the recommendations of a model if the estimates turn out to be wrong.6. Enlightened future managers do not need to know which of the following?A. How the models of management science are solved.B. When management science can and cannot be applied.C. How to apply the major techniques of management science.D. How to interpret the results of a management science study.E. None of the above.7. Which of the following is not a component of a mathematical model for decision making?A. Decision variables.B. A spreadsheet.C. Constraints.D. Parameters.E. All of the above.8. Which of the following is not a step taken in a typical management science study?A. Define the problem and gather data.B. Formulate a model.C. Apply the model and develop recommendations.D. Help to implement the recommendation.E. All of the above are typical steps in a management science study.9. Which of the following is true at the break-even point?A. The fixed cost equals the variable cost.B. The production quantity equals the sales forecast.C. The company will neither make nor lose money on the product.D. The profit equals the cost.E. None of the above.10. A constraint in a mathematical model isA. a variable representing the decision to be made.B. an inequality or equation that restricts the values of the variables.C. a measure of the performance of the model.D. the sales forecast.E. none of the above.Chapter 21. Linear programming problems may have only one goal or objective specified.2. A feasible solution is one that satisfies at least one of the constraints of a linear programming problem.3. The cell containing the measure of performance is referred to as a changing cell.4. A linear programming problem can have only one optimal solution.5. When solving a maximization problem graphically, it is generally the goal to move the objective function line in, toward the origin, as far as possible.6. In a linear programming spreadsheet model, the output cells can typically be expressed as a SUMPRODUCT function.7. Changing only the right-hand side of a constraint creates parallel constraint boundary lines.8. The Assume Nonnegative option assures that the target cell will remain nonnegative.9. Which of the following is a component of a linear programming model?A. Constraints.B. Decision variables.C. Parameters.D. An objective.E. All of the above.10. Which of the following are not types of cells in a linear programming spreadsheet model?A. Changing cellsB. Target cellC. Output cellsD. Input cellsE. Data cells11. For the products x and y, which of the following could be a linear programming objective function?A. C = x + 2y.B. C = x+ 2xy.C. C = x - 2(y-squared).D. C = x + 2x/y.E. All of the above.12. Which of the following is not a step in the graphical method:A. Draw the constraint boundary line for each functional constraint.B. Find the feasible region.C. Determine the slope of one objective function line.D. Find the optimal solution using a straight-edge.E. All of the above are steps in the graphical method.13. Given the following 2 constraints, which solution is a feasible solution for a maximization problem?A. (X1 , X2 ) = (1, 5).B. (X1 , X2 ) = (4, 1).C. (X1 , X2 ) = (4, 0).D. (X1 , X2 ) = (2, 1).E. (X1 , X2 ) = (2, 4).14. What is the cost of the optimal solution for the following problem?A. 0.B. 3.C. 15.D. 18.E. 21.15. A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. What is the objective function?A. 2B + 4C <= 4,800.B. (B, C) = (0, 1400).C. P = 0.2B + 0.3C.D. $340.E. None of the above.Chapter 31. There is only one correct way to set up a spreadsheet model.2. In the Everglade Golden Years Company problem, the long-term loan had a lower interest rate than the short-term loan.3. When sketching out a spreadsheet, all of the equations should be entered in the sketch.4. Data should be repeated on the spreadsheet wherever it is needed.5. Numbers should be entered directly into formulas.6. Range names can make equations and the Solver dialogue box easier to read and interpret.7. Shading of cells in the spreadsheet should be avoided.8. The toggle alternates between showing equations and showing values in the cells of the spreadsheet.9. Powerful Excel functions should be used to keep the spreadsheet as concise as possible.10. Using absolute and relative references appropriately makes it easy to expand a model to full-size.11. Which of the following is not a major step in the process of modeling with spreadsheets?A. PlanB. BuildC. TestD. AnalyzeE. All are major steps in the process of modeling with spreadsheets.12. Which of the following are useful steps in the planning stage?A. Visualize where you want to finishB. Do some calculations by handC. Sketch out a spreadsheetD. Sensitivity analysisE. All are useful steps in the planning stage.13. Each constraint should be entered into how many cells on the spreadsheet?A. 1B. 2C. 3D. 4E. 514. Which of the following is not useful for debugging a spreadsheet?A. The auditing toolbar.B. The toggle.C. Trying different values in the changing cells for which you know the solution.D. A and C only.E. All are useful for debugging a spreadsheet.15. Which element of the spreadsheet model should be entered first?A. The data.B. The output cells.C. The target cell.D. The changing cells.E. None of the above.Chapter 41. When formulating a linear programming model on a spreadsheet, the constraints are located in the data cells.2. A mathematical model will be an approximation of the real problem.3. Linear programming must have integer solutions.4. Strict inequalities (i.e., < or >) are permitted in linear programming formulations.5. Once a linear programming problem has been formulated, it is common to make major adjustments to it.6. Resource-allocation problems have constraints for each limited resource.7. A resource constraint has a >= sign in a linear programming model.8. Distribution-network problems typically have mostly <= constraints.9. Which of the following is not a category of linear programming problems?A. Resource-allocation problems.B. Cost-benefit-tradeoff problems.C. Distribution-network problems.D. B and C.E. All of the above are categories of linear programming problems.10. A linear programming model does not contain which of the following components?A. Data.B. Decisions.C. Constraints.D. Measure of performance.E. A spreadsheet.11. Which of the following may not be in a linear programming formulation?A. <=.B. >.C. =.D. A. and C. only.E. All of the above.12. Distribution-network problems have the following type of constraints:A. >=.B. <=.C. >.D. <.E. None of the above.13. Resource-allocation problems typically have which of the following type of constraints:A. >=.B. <=.C. =.D. None of the above.E. All of the above.14. Cost-benefit tradeoff problems typically have which of the following type of constraints:A. >=.B. <=.C. =.D. None of the above.E. All of the above.15. Mixed problems may not have which of the following type of constraints:A. >=.B. <=.C. =.D. All of the above.E. None of the above.Chapter 61. Transportation problems are concerned with distributing commodities from sources to destinations in such a way as to maximize the total amount shipped.2. Transportation problems always have integer solutions if the supplies and demands are all integer.3. The Hungarian Method is an algorithm used to solve assignment problems.4. When demand and supply are not equal in a transportation problem then the problem can be reformulated and solved.5. It is possible to adjust the transportation simplex method to maximize profit instead of minimize cost.6. Which of the following is needed to use the transportation model?A. Capacity of the sources.B. Demand of the destinations.C. Unit shipping costs.D. All of the above.E. None of the above.7. Which of the following is not an assumption or requirement of a transportation problem?A. I and IVB. II and IIIC. I, II and IVD. I and IIIE. I, II, III, and IV8. Which of the following can be modeled as variants of the standard transportation problem?A. The sum of the supplies exceeds the sum of demands.B. A destination has a minimum and maximum demand.C. Certain source-destination combinations cannot be used for distributing units.D. A. and B. only.E. All can be modeled as a variation of the transportation problem.9. An assignment problem:A. will always have an integer solution.B. has all supplies and demands equal to 0.C. always has the demand greater than the supply.D. All of the above.E. None of the above.10. Which of the following is an assumption of assignment problems?A. The number of assignees and the number of tasks are the sameB. The objective is to minimize the number of assignments not made.C. Each task is to be performed by exactly one assignee.D. A. and C. only.E. None of the aboveChapter 71. Each node in a minimum cost flow problem where the net amount of flow generated is a fixed positive number is a supply node.2. If the SUMIF function is used in a network optimization models, it will be nonlinear.3. In a maximum flow problem, the source and sink do not have fixed supplies and demands.4. A shortest path problem may have multiple destinations.5. The number of links in a spanning tree is always the same as the number of nodes.6. The network simplex is a streamlined version of the simplex method.7. Which of the following is not a special type of linear programming problem?A. I and IV.B. I, II, and III.C. II, III, and IV.D. IV only.E. None of the above.8. Which of the following will have positive net outflow in a minimum cost flow problem?A. Supply nodes.B. Transshipment nodes.C. Demand nodes.D. All of the above.E. None of the above.9. Which of the following is not an application of a shortest path problem?A. I and II onlyB. I, II, and III only.C. II onlyD. I, II, III, and IVE. I, III, and IV only.10. If there are 8 nodes in a minimum spanning tree problem then how many links will there be in the solution?A. 6.B. 7.C. 8.D. We cannot tell how many links there will be until it has been solved.E. The total cost will be 7.Chapter 81. In an Activity-On-Arc project network, the nodes are used to separate an activity from each of its immediate predecessors.2. If two paths are tied for the longest duration, the one with the most activities would be considered to be the critical path.3. The slack of an activity is the difference between the latest finish and the latest start times.4. When calculating the probability that a project will finish by a certain time, the approximation that is obtained is usually higher than the true probability.5. The latest finish time for an activity is:A. based on the length of the critical path.B. determined by the maximum of the earliest finish times of its immediate predecessors.C. determined by the maximum of the earliest finish times of its immediate successors.D. the same as the latest start time of its immediate predecessor.E. None of the above.6. Activity C has an early start time of 7, an early finish time of 12, a latest start time of 13, and a latest finish time of 18. Its slack is:A. 0.B. 1.C. 4.D. 6.E. 9.7. Which of the following is a benefit of PERT/CPM?A. It provides an estimate of how long a project will take.B. It allows an activity to overlap with its immediate predecessors.C. It addresses the important issue of how to allocate limited resources.D. A. and C. only.E. All of the above.8. An activity has an optimistic time estimate of four days, a most likely time estimate of eight days, and a pessimistic time estimate of fifteen days. The expected duration of this activity is:A. 7.0 days.B. 7.5 days.C. 8.0 days.D. 8.5 days.E. 10.0 days.9. Which of the following is not a way of crashing an activity?A. Using overtime.B. Hiring more workers.C. Using specialized equipment.D. A. and C.E. All of the above are ways of crashing an activity.10. PERT/Cost does not:A. find the penalty costs if a project is not completed on time.B. compare the actual budget with the planned budget.C. show management where to focus attention during the project.D. A. and B. only.E. B. and C. only.Chapter 91. In an integer programming problem, all of the decision variables are not necessarily required to be integer values.2. Solving the LP relaxation of an integer programming problem and rounding the solution will always find the optimal solution.3. Binary integer programming problems are those where all the decision variables are restricted to integer values.4. Variables whose only possible values are 0 and 1 are called binary variables.5. A problems where all the variables are binary variables is called a mixed BIP problem.6. If choosing one alternative from a group excludes choosing all of the others then these alternatives are called complimentary.7. The constraint x1 +x2 +x3 <= 1 in a BIP represents mutually exclusive alternatives.8. Solving the LP relaxation of an integer programming problem and rounding the solution will find a solution that may not be:A. feasible.B. optimal.C. integer.D. A. and B.E. All of the above.9. Binary integer programming problems can answer which types of questions?A. How much of a product should be produced?B. Should an investment be made?C. Should a plant be located at a particular location?D. All of the above.E. B. and C. only.10. Binary variables can have the following values:A. 0.B. 1.C. any integer value.D. A. and B. only.E. All of the above.11. In a BIP problem with 3 mutually exclusive alternatives, A, B, and C , the following constraint needs to be added to the formulation if two alternatives must be chosen:A. A + B + C <= 2.B. A + B + C = 2.C. A - B - C <= 2.D. A + B + C <= 1.E. None of the above.12. In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If project S can be undertaken only if project T is also undertaken then the following constraint needs to be added to the formulation:A. S + T <= 1.B. S + T = 1.C. S <= T.D. T <= S.E. None of the above.13. In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are 3 projects under consideration (A, B, and C) and at most 2 can be chosen then the following constraint needs to be added to the formulation:A. A + B + C <= 3.B. A + B + C <= 2.C. A + B + C >= 2.D. A + B + C = 2.E. None of the above.14. Auxiliary binary variables can be used to deal with:A. set-up costs for initiating production.B. mutually exclusive products.C. either-or constraints.D. All of the above.E. None of the above.Chapter 101. If the slope of a curve on a profit graph never increases but sometimes decreases as the level of the activity increases, then it is said to have increasing marginal returns.2. The Solver Table can be used to try a variety of starting points in a nonlinear programming problem.3. Separable programming requires that the objective function be piecewise linear.4. The Evolutionary Solver uses an algorithm that is sometimes called a genetic algorithm.5. Evolutionary Solver is a good choice for problems with many constraints.6. The Evolutionary Solver requires that the constraints all be linear.7. Problems with increasing marginal returns are generally easier for Solver to solve than problems with decreasing marginal returns.8. A nonlinear programming problem will have how many local maxima?A. 0B. 1C. 2D. 3E. It can have any number of local maxima.9. A linear function may not contain which of the following?A. A term that contains a single variable with an exponent of 1.B. A term that contains a single variable with an exponent of 2.C. A term that is a constant times the product of two variables.D. B. and C. only.E. All of the above.10. Which of the following Excel functions are linear (assuming changing cells are in C1:C6 and data cells are in D1:D6):A. I only.B. I and II.C. I and III.D. II and IV.E. III and IV.11. Which of the following Excel functions are linear (assuming changing cells are in C1:C6 and data cells are in D1:D6):A. I only.B. I and II.C. II and III.D. I and IV.E. IV only.12. Which of the following is an example of a nonlinear function?A. P= 5 X1+ 7 X2 - 2 (X2-squared).B. P= 8 X1 - 4 X2.C. P= X1 + 6 X2 + 3 X1 X2.D. A. and C. only.E. All of the above.13. The requirement that each term in the objective function only contains a single variable is referred to as:A. the proportionality assumption.B. the divisibility assumption.C. the additivity assumption.D. a nonlinear function.E. None of the above.Chapter 111. The overall objective for a goal programming problem is to determine the most important objective in the problem.2. Goal programming provides two alternative ways of formulating problems with multiple goals: preemptive and weighted goal programming.3. Preemptive goal programming is an appropriate technique when all of the goals are fairly equal in importance.4. In preemptive goal programming it is assumed that there is a distinct order of importance for all goals, and that no goals are of equal importance.5. Preemptive goal programming involves solving a single linear programming model.6. Weighted goal programming involves solving a single linear programming model.7. Goal programming can handle problems with how many different objectives or goals?A. 1.B. 2.C. 3.D. 4.E. Any number of objectives or goals.8. Which of the following are included as changing cells in a goal programming formulation?A. The levels of the various activities.B. The amount over each goal.C. The amount under each goal.D. B. and C. only.E. All of the above are changing cells.9. In weighted goal programming the objective is toA. Maximize profit.B. Minimize cost.C. Achieve the most important goal.D. Minimize a weighted sum of deviations from the various goals.E. Minimize the amount under each goal.10. In preemptive goal programming, the most important thing is toA. Achieve the most important goal.B. Come close to achieving all the goals.C. Ignore the least important goal.D. A. and C.E. All of the above.Chapter 121. Prior probabilities refer to the relative likelihood of past events.2. Bayes' decision rule says to choose the alternative with the largest possible payoff.3. The EVPI indicates how much the payoff will be with perfect information.4. A risk seeker has an increasing marginal utility for money.5. The exponential utility function assumes a variable aversion to risk.6. The maximax criterion is appropriate for the eternal optimist.7. The expected payoff is the payoff that is most likely to occur.8. In a decision tree, the expected payoff of a particular event node is equal to the SUMPRODUCT of the probabilities and expected payoffs of each branch.9. Sensitivity analysis of a decision tree requires the use of Solver Table.10. If C > EVPI then it is not worthwhile to obtain more information.11. Which of the following statements is correct when making decisions?A. The sum of the state of nature probabilities must be 1.B. Every probability must be greater than or equal to 0.C. All probabilities are assumed to be equal.D. A. and B. only.E. All of the above.12. Given the following information what is the maximum likelihood strategy?A. A.B. B.C. C.D. D.E. E.13. Given the following information what is the Bayes' decision rule strategy?A. A.B. B.C. C.D. D.E. E.14. Given the following information what is the expected value of perfect information?A. 4.5.B. 9.C. 40.5.D. 49.5.E. 60.15. Which of the following can be used to do sensitivity analysis with decision trees?A. Trial and error.B. A Data Table.C. SensIt.D. A. and C.E. All of the above.答案：chapter 1Chapter 1 ABABA ABECBChapter 2 ABBBB AABED AEDDCChapter 3 BABBB ABABA EDCEAChapter 4 BABBA ABBEE BEBAEChapter 6 BAAAA DBEADChapter 7 ABABB BDACBChapter 8 ABBAE DADEAChapter 9 ABBAB BADED BCDEChapter 10 BABAB BBEDC EDCChapter 11 BABBB AEEDAChapter 12 BBBAB ABABA DCCBE。

Chap04.ppt

The Answer Report
See file Fig4-1.xls
The Sensitivity Report
See file Fig4-1.xls
X2
250
How Changes in Objective Coefficients Change the Slope of the Level Curve
Alternate Optimal Solutions
Values of zero (0) in the “Allowable
Increase” or “Allowable Decrease” columns for the Changing Cells indicate that an alternate optimal solution exists.
See file Fig4-4.xls
Other Uses of Shadow Prices
Suppose a new Hot Tub (the Typhoon-Lagoon) is being considered. It generates a marginal profit of $320 and requires:
Shadow prices for nonbinding constraints are always zero.
Comments About Changes in Constraint RHS Values
Shadow prices only indicate the changes that occur in the objective function value as RHS values change.
than it could otherwise do.

RebarCAD 3D和标记的建筑信息模型(BIM)解决方案：从设计意图到梁条建模说明书

CS322752CADS RebarCAD 3D and Markup: The BIM Solution from Design Intent to Rebar ModelingJohn KochummenCADS Software India Pvt. LtdJason ColcombeCADS LtdLearning ObjectivesLearn how to prepare a rebar intent markup from design results, and how to model the design reinforcement and enhance it to a practical 3D rebar model Learn how to work collaboratively within a federated model in BIM 360, and produce 2D fabrication drawings from the 3D modelLearn how to automate rebar modeling using CADS Rebar Extensions, and Prepare Bar Bending Schedules Manage revisions in BBSLearn how to prepare custom Excel reports, and production output files for automated rebar fabricationDescriptionRebarCAD 3D provides an excellent and comprehensive set of tools to perform the crucial task of placing and detailing reinforcement in a Revit model, staying true to the BIM philosophy. We’ll demonstrate an efficient workflow: Start with a structural model; create design reinforcement; mark up the model with design intent; and end with a detailed rebar model, fabrication drawings, rebar schedules, and production output files from RebarCAD 3D. We’ll also demonstrate the revision management in rebar schedule and automated rebar modeling using CADS’ Rebar Extensions.Speaker(s)John Kochummen CADS Software India Pvt. Ltd. Product Manager – RebarCAD 3DJason Colcombe CADS Ltd - CADS RC3D Senior Product SpecialistPage 1Page 2IntroductionRebarCAD 3D for Revit has been designed to enhance the placement, annotation and bar marking of rebar in 3D structures. The software provides functionality to create 2D detail drawings and bar bending lists to acceptable standards.Additional annotation functions have been created to detail tapered ranges and markrebar ends.Enhanced layering tools allow rebar to be split into zones within a structure, rebarvisibility can be controlled using layer assignment.Editing functions allow rebar to be copied from one structure to another. Rebar can be ‘joined’ together to form new bar shapes.Rebar can be trimmed and extended to openings, detail or model lines.Openings in the structure can be identified and trimming reinforcement added. Path placement functions allow the rebar to be placed parallel to other rebar in thestructure.Rebar can be assigned to a structure, release and drawing sheet. Manage the rebaraccording to these assignments. Currently, the release of rebar for production is manually controlled.The Rebar Lists can be placed on drawing sheets or printed using industry standardtemplates. The bar list templates are easy to customise to company standards.Page 3RebarCAD 3D/CADS RC3D - From Zero to Hero in under 5 minutesIn this quick exercise we will demonstrate how to use the most frequent tools to get massplaced Revit reinforcement into a detailing environment and automatically create a Bar Bending Schedule.We will take an irregular shaped slab and add Area Reinforcement to the slab using the default Revit Reinforcement Tools.Area Rebar is held within an Area System so cannot be edited individuallyRear is Hidden by default and need to be edit via the Properties Palette > View Visibility StatesThe first Tool to apply is the Assign Reinforcement Layer , this not only applies the Layer Naming Conventions in the Revit Reinforcement Settings but automatically makes all Rebar Visible in ViewReinforcement Settings can be found on the RebarCAD 3D Tab > Reinforcement Panel > Drop-Down ArrowChange the settings for Area/Path/Varying Rebar Set to meet company standards or save to a TemplatePage 4You can work on different layers using Rebar Visibility where and when required or create new layers outside the standard Revit Reinforcement SettingsIf you do need to manually apply a new Reinforcement Layer simply use the “Assign Reinforcement Layer” Tool Select the Rebar and either pick from the drop down list or manually enter a new Layer nameFrom here we can now Splice Rebar in the Top Major (T1) and Minor (T2) bar lengths and edit the “Stock Length” manually if they do not follow standard stock length rules in the Project Settings.The information used in the Rebar Splice Dialogue is driven by the Project Settings > Rebar DimsYou can either use the defaults of manually edit the fields as required.Page 5One of the consequences of removing the “Area System” is Varying Rebar Sets are converted to single rebar elements – We can simple convert this back by using Varying RebarReinforcement Settings can be found on the RebarCAD 3D Tab > Reinforcement Panel > Drop-Down Arrow Change the settings for Area/Path/Varying Rebar Set to meet company standards or save to a TemplateAbove is an example of single rebar converted to a Varying Free Form Set using the Varying Range Tool. You can also “Step Taper” rebar from the same Tool drop-down in the CADS RC3D RibbonPage 6Once the bars have been spliced and spilt ranges reformed we can simply use the Annotation Tool to select the Host and automatically create all bar range tag in once process.Host are Structural Elements/Families that allow the placing of rebar within the. If you select a Host and the Rebar option is not available from the Contextual Tab on the Ribbon it is more than likely not a Structural Elements/Family. In-Place Families can also allow rebar placement if the “Can Host Rebar” option it ticked in the Properties Palette during creation.To create a Schedule we first need to assign the Host Mark to the Slab –Select the Slab > Properties Palette > MarkHost Marks are similar to Assign Member in RebarCAD/CADS RC. Revit Rebar uses the Host Mark as a directreference and is essential for breaking Schedules down into elements lists.Page 7Using the Assign Drawing Sheet you can now select the rebar you wish to be designated to Sheet Reference, this allows you to filter the rebar as and where required automatically.There are several methods of creating Schedules:Place = Puts the Schedule directly onto a Sheet (created using a CADS Family Titleblock or use a predefined Titleblock)Excel = Export to an Excel Spreadsheet (These can be manually edited for you needs) Print = Creates a New Sheet with the Schedule in placeShow Schedule = New Scheduling System held within its own environment.We are using Place in this example. Define the properties within the Bar List dialogue and then position the outline onto the Sheet.If there is more than one Sheet in the Schedule you need to finish the placement of all Sheets before it will generatethe information. This is common if you choose to show ALL Sketches and not First Instance Only.Page 8The Schedule is now automatically created on the Sheet showing the information from the setting selected in the Bar List dialogue.The units used are determined by the Revit Project Units in the Manage TabThat’s your 5 minutes up!The next few pages will cover some simple editing functions in our 2 Minute Tip SectionPage 9Once Revit Reinforcement Area Systems are removed editing ranges/sets becomes increasing time consuming in Revit so RebarCAD 3C/CADS RC3D has added tools to assist with the process.Trimming Bars around new opening – Trim/Extend RebarThis opening has been added after the aforementioned process in the 5 minute challengeSelect the Slab > Click Finish in the Option Bar > Click on the Edges to use for Trimming > Finish in the Options Bar > either manually select bars or use Multiple to draw fencing linesAny Revit lines can be used for cutting/extensions planes.Page 10We can add automatic Opening Reinforcement to any openings within Slabs and Walls. Select the Slab > Click in the Opening > Esc. > Enter information in dialogueThis can be used on one or more openings.When changes have been made you can Audit the view to ensure there are no bars visible that have not been accounted for in the Schedule to prevent incorrect quantities against issued drawings.Audit can also be used for Stock Length checks and Untagged and Duplicate Annotations/Labels/Tags.Page 11In this example we may have multiple elements on project but do not wish to model the rebar for them all so we can use Host Count Override – below is a Schedule using Place for a Pad Base (Pad A2) and Starter Bars into a Column (CA2)Note the Settings/Options selected in the Dialogue *Show title block, *Use host count override.We now apply the Host Count Override and when placing the Schedule this time we use the OOTB Revit Rebar Schedule Titleblock Family.Note the Settings/Options selected in the Dialogue *Show title block, *Use host count override.Page 12 In the NEW Show Schedule System I have created a revised Schedule to indicate the Pad Base as per the above example and Issued it to ensure sure it is locked any changes are recorded.You can use existing company RebarCAD/CADS RC Schedule Templates and Excel Templates within the New Scheduling SystemI will remove one set of bars and edit the spacing of another ranges, and on reopening the New Scheduling System you will see the Bars that have been deleted are struck-through and those that have been changed show a Revision Mark next to them.You can set which revisions you wish to show and the format in the Edit Schedule locally or Settings for global changes and for futures Schedule creation.。

APseudo-RandomNumberGeneratorforSpreadsheets

A Pseudo-Random Number Generator for SpreadsheetsResearch Note, Jan 2013Michael Lampton, Space Sciences Lab, UC BerkeleyAbstractSetting up a spreadsheet to simulate noisy data collection from an experiment requires a generator of pseudo-random numbers. The function RAND built into popular spreadsheets is unsuitable because it rerandomizes every time the spreadsheet is recalculated. Unlike measured data, RAND changes for each data analysis activity. Moreover, spreadsheet rootfinding plugins necessarily recalculate the entire spreadsheet for each internal iteration, and RAND cannot keep its output constant during a sequence of iterations. Beyond that there is no way to enforce a common seed, to verify agreement between instructor and student statistical results. Here, I introduce a well-tested random number generator that overcomes these limitations and I show how to make it portable to spreadsheets and high-level computer languages. Keywords: random numbers, spreadsheets.----GoalsFor decades, physics instructors have used spreadsheets to organize computational work in the classroom and laboratory. To statistically model measurement errors, some kind of pseudo-random number (PRN) generator is essential. Desirable features of a simple spreadsheet-based PRN generator (PRNG) are: • Occupies a single spreadsheet cell;• Specifies a single input cell for its argument or seed;• Output spans 0<x<1 for use with distribution generators NORMINV, TINV, etc.;• Has a period that far exceeds the likely number of rows in an experiment simulator;• Has correct means, variances, uniformities, and autocorrelations;• Has a white (flat) power spectrum;• Pseudo-random sequences (PRSs) from different seeds should be statistically orthogonal;• For the same seed, different spreadsheets should yield the same PRS;• Should also be portable between spreadsheets and high level languages.Generators designed for cryptography must pass exceedingly demanding tests; see L’Ecuyer (2010) and references therein for examples of current approaches. Those generators are complex. In contrast, a simple seed-controlled PRNG good for thousands (not billions!) of iterations would be a useful spreadsheet component. In this Note, I write the Lewis-Goodman-Miller (LGM) generator in spreadsheet form and show how to seed it, as an aid to those who need a fully controlled source of PRNs to model experimental noise or measurement errors. L’Ecuyer (2001) offers test results comparing a variety of popular RNG implementations, including this one.A fully portable generatorThe most popular simple PRN generators are based on the multiplicative linear algorithm originally by Lehmer (1949); see also Lewis Goodman and Miller (1969), Wichmann and Hill (1982), Park and Miller (1988), Press,Flannery, Teukolsky, and Vetterling (1988), Knuth (1997), L'Ecuyer (2001), and Wichmann and Hill (2006). This generator receives an integer Zin and produces an integer Zout:Zout = (A·Zin) modM (1)Briefly, the low order bits of the input integer Zin are hoisted to higher significance by an integer multiplier A, and the highest order bits are discarded by the modulus operation. The modulus M sets the finesse of the comb of output values. If M and A are properly chosen, the period of the sequence will have the maximum possible length of M- 1. Owing to its speed and simplicity it has enjoyed a long life and has been ported to a variety of environments. Obviously it must never be given a seed of zero, or the whole sequence would collapse. Indeed, seed values very near zero cause the first few iterates to be substandard in size (see Wichmann and Hill (2006)), and seeds must be randomized if the PRS is to have a random looking startup sequence. I offer a seeder in the next section.Exact integer arithmetic is essential if a generator is to be portable. The IEEE-754 double precision specification requires exact integer arithmetic in the range -252to +252-1 and this standard is widely obeyed by high-level languages. However, spreadsheets typically deliver exact integer arithmetic only for numbers whose size is less than about 1015 i.e., fifteen digits accuracy or about 250 (see Almiron et al. 2010). To avoid overflow, a PRN algorithm internal integer product A·M should be comfortably smaller than this fifteen-digit bound.A second requirement is that the generator must deliver variates in the range 0 < Z < 1 so that these can be fed into the appropriate inverse distribution generator, for example NORMINV or TINV spreadsheet functions. This requirement is customarily met by moving Equation 1 into a floating point environment, with M·Zin playing the role of the integer Zin:Zout = ((M·A·Zin) modM)/M (2)I adopt the Lewis-Goodman-Miller (1969) “minimal standard generator" (see Park and Miller 1988) defined by the constantsM = 231-1 = 2147483647 (3a)(3b)A = 75=16807This generator has been exhaustively tested and has been found to be generally acceptable within its limited sequence length of M-1. This generator will be portable among systems whose arithmetic correctly handles numbers of magnitude A·M without loss of integer accuracy. Here, the largest number that has to be handled is the MA product, about 3.6E13. This is comfortably within the 15-digit accuracy of all popular spreadsheets. Features of this PRNG are:• Successive iterates are uncorrelated;• Beyond that, they pass the Knuth spectral test for dimensions 2,3,4,5, and 6;• The PRNG is maximal length (here equal to M-1);• The PRNG populates the variate axis uniformly;• The PRNG is portable: it delivers the same PRS on every platform.In a spreadsheet cell, Equation 2 is implemented with the expression=MOD(ROUND(M*A*Z,0),M)/M (4)Again, M and A are the constants from Equation 3. Z stands for the address (column,row) of whichever cell contains the previous RN in your sequence, or, for the initial RN, it is the address of your seed generator. The ROUND(X,0) operation is essential for portability: it reestablishes the correct integer product by removing the floating point division errors (order of 10-15) that arise in the previous iteration division. Without ROUND(), the PRS would depend on the chain of division errors which wouldintroduce fractional terms into the sum. These fractional terms differ among spreadsheets and can also differ from the IEEE-754 oating point specifications, causing the various platform PRSs to diverge after some number of iterations.Portable seedingHow should this function be seeded? In experiment modeling, users will want a selection ofseeds that deliver independent statistics. The entire PRS period is about two billion, so ifeach segment has 1000 iterates, any randomly chosen seed will have only one chance in amillion of overlapping any other given seed segment. Very good odds! but of course the RNGis totally deterministic and the seeder must be verified for freedom from overlap. Fractionalseeds are essential since all integer inputs are equivalent to zero seed and yield the same nullPRS.A good seeder will accept an integer run number and deliver a prerandomized seed value. (A simple list of seeds like 0.1, 0.2, etc., would fail the portability test because they are unlikely to be found among the comb of PRS values.) A prerandomized seed makes the PRNG self-starting, requiring no warm-up iterations before use. I address this issue here by offering an explicit seed() function that accepts an integer run number IRUN=1, 2, ... and delivers a starting point for a PRS. For portability, I precondition the seed by applying the same modulus treatment that each RN has:=MOD(ROUND(MOD(IRUN*EXP(1),1)*M*A,0),M)/M (5) Here, the constant EXP(1)=2.71828... supplies some fractional digits that are boosted by the integer run number IRUN. That fractional part is then boosted by the MA product to fill the working span of double precision integers. That product is then reduced modulo M, and normalized to unit span in the same way that PRS numbers are reduced, so that each seed is a member of the PRS comb. These actions make every seed compute the same way on all platforms.Portability CheckPark and Miller (1988) emphasize that exhaustive statistical testing is exceedingly demanding of resources (see for example Fishman and Moore (1986)) and recommend that any portable RNG should be tested for correctness rather than for its statistics. For the constants in Equation 3 above and a seed derived from IRUN=1, iteration 10000 should yield Z = 0.785320384794. I verified this result for Microsoft Excel 2007 (PC edition), Gnome Gnumeric 1.10.16, Open Office Calc 3.3.0, Java 1.5.0, Gnu C, and Python 2.6.6. Portions of these runs are listed in Table 1 below. All platforms tested are in agreement over the range of parameters tested, giving good evidence of portability.Table 1: Iterations on Various Platforms1 2 3 999 IRUN=Seed= 0.162690911052 0.325381822570 0.488072733622 0.528220262159 iter=1 0.346142053300 0.692291932969 0.038433986268 0.797946102357 Exceliter=2 0.609489807212 0.350517402566 0.960007209778 0.080142321568 Exceliter=3 0.695189804628 0.145984931451 0.841174736079 0.951998594195 Exceliter=4 0.0550******** 0.568742901352 0.623789286066 0.240372629482 ExcelExceliter=10000 0.785320384794 0.0566******** 0.841933686213 0.887922685076 iter=100000.785320384794 0.0566******** 0.841933686213 0.887922685076 Gnumericiter=10000 0.785320384794 0.0566******** 0.841933686213 0.887922685076 Calciter=10000 0.785320384794 0.0566******** 0.841933686213 0.887922685076 JavaTable 1: Demonstration of portability among platforms. For run numbers listed, PRS iterations 1, 2, 3, 4,and 10000 are shown to 12 digits accuracy. Iteration 10000 is shown for Excel 2007 (PC); Gnumeric (PC); OpenOffice3 Calc(Mac); and Java which is IEEE-754 compliant.Testing the seederAny PRS run should not overlap any portion of any other PRS run. The seeder generates a list of random-appearing seeds that start the PRSs. Figure 1 below shows the log of the maximum nonoverlapping PRS length as a function of the log of the number of runs (blue) and also (red) the maximum possible PRSlength if the segments were to be uniformly arranged.Figure 1: Plot showing the log of the maximum available sequence length without overlapping any other sequence as a function of the log of the number of seeds chosen. For 100 runs, individual sequences can have millions of iterations without overlap.A handy on-off switchI noted that IRUN=0 and its seed value of zero is prohibited because zero collapses the entire PRS. If however each PRN is used solely to feed an inverse cumulative probability function such as NORMINV, this all-zero off state can be recognized and employed to switch off the random deviations throughout the worksheet. Use the expression=IF(Z=0,0,NORMINV(Z,0,1)) (6)where Z is again the (column, row) address of the uniform PRN being converted.ConclusionsIn Equations 4 and 5, I have presented a portable uniform random number generator that is under user control: its variates are e_ectively random and independent for a wide range of seed values, but then | like real measurements | they become constant during subsequent data analysis. Background theory shows good performance for small scale simulation situations found in the classroom and laboratory.AcknowledgmentThe author greatfully acknowledges the support by the Director, Office of Science, U.S. Department of Energy under Contract No. DE-AC03-76SF00098.ReferencesAlmiron MG, et al. (2010). “On the Numerical Accuracy of Spreadsheets." J. Stat. Software, 34(4), 1-24. Fishman GS, Moore LR (1986). “An Exhaustive Analysis of Multiplicative Congruential Random Number Generators with Modulus 231-1" SIAM J. Scientific and Statistical Computing, 7, 24-45.Knuth DE (1997). “The Art of Computer Programming, volume 2: Seminumerical Algorithms.”3rd edition. Addison Wesley, Reading, Massachusetts.L’Ecuyer P (2001) “Software for Uniform Random Number Generation: Distinguishing the Good and the Bad,” Proceedings of the 2001 Winter Simulation Conference, IEEE Press, Dec. 2001, 95-105.L'Ecuyer P (2010), ``Pseudorandom Number Generators'', in Encyclopedia of Quantitative Finance,R. Cont, Ed., in volume Simulation Methods in Financial Engineering, E. Platen and P. Jaeckel Eds., John Wiley, Chichester, UK, 1431-1437.Lehmer DH (1949). “Mathematical Methods in Large-scale Computing Units." Proc. 2ndSymposium on Large-Scale Digital Calculating Machinery, pp. 141-146; also Annals of the Computation Laboratory of Harvard University, v.26 (1951).Lewis PAW, Goodman AS, and Miller JM (1969) “A pseudo-random number generator for theSystem/360,” IBM Systems Journal v.8 136-143.Park SK, Miller KW (1988). “Random Number Generators: Good Ones are Hard to Find." Communications of the ACM, pp. 1192-1201.Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1988). “Numerical Recipes” 2nd edition. Cambridge University Press.Wichmann BA, Hill ID (1982). “Algorithm AS183: An Effcient and Portable Pseudo-Random Number Generator." Applied Statistics, 31(2), 188-190.Wichmann BA, Hill ID (2006). “Generating Good Pseudo-Random Numbers." Computational Statistics and Data Analysis, 51(3), 1614-1622.。

dca曲线的计算方法

dca曲线的计算方法The DCA (Discounted Cash Flow Analysis) curve is a vital tool in finance for evaluating the performance and value of an investment over time. DCA曲线是金融领域中用来评估投资绩效和价值的重要工具。

It is a graphical representation of the relationship between the discount rate and the net present value of an investment. 这是一种图形化的表示，显示了贴现率与投资的净现值之间的关系。

A DCA curve is constructed by plotting different discount rates along the x-axis and the corresponding net present values along the y-axis. 通过在x轴上绘制不同的折现率和在y轴上绘制相应的净现值来构建DCA曲线。

The resulting curve provides valuable insights into how changes in the discount rate impact the value of the investment. 结果曲线可以为我们提供有价值的信息，指导我们了解折现率的变化如何影响投资的价值。

One common approach to calculating the DCA curve is to use a spreadsheet program, such as Microsoft Excel, to input the cash flows and discount rate, and then generate the corresponding net present values for different discount rates. 一种常见的计算DCA曲线的方法是使用电子表格程序（如Microsoft Excel）来输入现金流和折现率，然后生成不同折现率对应的净现值。

Statistics and Decision Science - Lecture 01

LP Model for Blue Ridge Hot Tubs
MAX: 350X1 + 300X2 S.T.: 1X1 + 1X2 <= 200 9X1 + 6X2 <= 1566 12X1 + 16X2 <= 2880 X1 >= 0 X2 >= 0
General Form of an Optimization Problem
– Oil in the earth – Land for dumps – Time – Money – Workers
Mathematical Programming...
MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business. a.k.a. Optimization
X2
250
Plotting the First Constraint
(0, 200)
200
boundary line of pump constraint
150
X1 + X2 = 200
100
50
(200, 0)
0
0
50
100
150
200
250
X1
X2
250
Plotting the Second Constraint
100
(100, 0)
50
0 0 50

implementationof...

The Informatics Interchange column give s re ade rs an opportunity to share their experiences with information technology in pharmacy. AJHP re ade rs are invite d to submit the ir e xpe rie nce s and pe rtine nt le ssons-learned related to pharmacy informatics. Topics should focus on the use of information te chnology in the me dication-use proce ss, informatics pearls, informatics education and research, and information technology management. Readers are invited to submit their ideas or articles for the ***************************, c/o Allie Woods at 7272 Wisconsin Avenue, Bethesda, MD 20814 (301-657-3000).Implementation of clinical decision support rulesEstablishment of a standardized process can be ben-eficial when implementing clinical decision sup-port (CDS) rules in the electronic health record (EH R). Postimplementation monitoring is an important step in evaluating the clinical value of CDS rules in improving outcomes.At the outset of efforts to implement a fully integrated EHR with computerized prescriber order entry, the EHR implementation team at Sharp H ealthCare researched the topic and concluded that a notable return on invest-ment with these initiatives would come from improve-ments in medication-use safety gained through the acti-vation of CDS functionality. After implementation of the EH R with CDS tools, including standardized order sets and allergy, drug–drug interaction, duplicate therapy, and dosage-range checking, the implementation team encountered a high demand for customized CDS rules and moved quickly to develop a process for managing the large volume of rule requests. This article describes the rule implementation process at our regional health-care delivery system.EHR functionality. During the “phased” rollout of the EHR at the system’s six inpatient facilities, the evidence-based medicine (EBM) team was responsible for con-verting all paper-based order sets to electronic versions at each hospital in preparation for the EHR go-live. The EBM team membership consisted of the corporate chief medical informatics officer (a physician), the corporate director of medical informatics (a physician), the cor-porate vice president of clinical informatics (a nurse), a corporate nurse informaticist (a nurse), and a corporate pharmacy informaticist (a pharmacist).As clinicians became familiar with EHR functionality, the information systems department (ISD) began to re-ceive a large number of requests for CDS rules to address additional opportunities for prescribing guidance. Re-quests were being submitted in numerous formats, and the number of requests was overwhelming. ISD manage-ment asked for assistance from the corporate clinical in-formatics (CI) team to collaboratively develop a process for rules submission, evaluation, and implementation. The CI team approached the EBM team to ask for assis-tance with managing these requests, since they had been through a similar process with order set conversion. The EBM team led the effort to establish a CDS rule imple-mentation process, with input provided by the CI team and the governing clinical effectiveness (CE) division, which oversees the corporate quality officers and the EBM and CI teams.CDS rule implementation process. Key steps identi-fied in the rule implementation process included the following:1. Formal definition of the problem to be addressed andthe purpose of the rule,2. Identification of the work group members submittingthe request,3. Preliminary programming to ensure the viability of therule logic within the EHR system programming and database structure,4. Testing of the completed rule to validate anticipatedresults,5. Background activation of the rule for preimplementa-tion auditing,6. Clinician education and announcement of the targetdate for implementation, and7. Postimplementation monitoring of the rule.The submission process was formalized by providing a standardized method for submission of proposed rules.F i g u r e . F o r m f o r s u b m i t t i n g a r e q u e s t f o r a c l i n i c a l d e c i s i o n s u p p o r t r u l e o p e n e d t o t h e “A p p r o v a l s ” t a b , w h i c h i n c l u d e s fi e l d s f o r i d e n t i f y i n g t h e P A R M I g r o u p (a c r o n y m d e fi n e d a t t o p o f t e m p l a t e ).A tabbed spreadsheet template was created as a submis-sion form (Figure). The form resulted from a process-improvement effort that addressed the backlog of all requests for EHR changes. Additional tabs listed annual corporate quality goals and provided a prioritization tool to aid the ISD management in determining which re-quest to address first when the number of requests was too great to fulfill with available programming resources. Rule requests were handled as a subset of EH R change requests, with routing of these requests to the EBM team. All corporate and hospital clinical informaticists were ed-ucated on the proper method of completion of the form. Form comple tion proce ss. To identify the reason for submission of a rule request, the submitter first completes the first tab of the form in order to provide situation, background, assessment, and recommendation (SBAR) information. Specifications, including EHR screen images and process flow diagrams, are posted on the second tab. Each rule request is considered a project, and the next tab is used to identify the “process owners” (i.e., the team re-questing the new rule), who will “own” and govern the rule during and after implementation. For each proposed rule, a group of people collectively referred to by the acronym PARMI (denoting process owners, approvers, resources, team members, and interested parties) is designated in the rule request. W ith the SBAR, specifications, and PARMI sections completed, the process owners submit the rule request by attaching the form to an e-mail message ad-dressed to all members of the EBM team.The EBM team monitors an e-mail account dedicated to handling rule requests on a weekly basis. Within 30 days of receipt of a request, the EBM team responds to the submitter, asking for more information (if necessary to complete the initial evaluation) and providing an up-date on the status of the request. When received, the EBM team does a high-level CDS “five-rights” review to deter-mine if the rule will have value by providing the right in-formation to the right person—in the right CDS interven-tion format and through the right channel—at the right time in the workflow, as described by Osheroff et al.1 The EBM team may also search the literature for evidence corroborating a request and supporting the clinical value of a requested rule.If the proposed rule meets the five-rights criteria and is deemed to have good potential for encouraging appro-priate prescribing, the ISD programming team begins the process of verifying that the EH R database contains an appropriate trigger to evoke the rule at the appropriate time and that the EH R programming logic can provide the desired result without adversely affecting EH R sys-tem response time. Programmers develop a set of options describing scenarios for available triggers, rule logic, and the result or action of the rule. The options, which are sent to the PARMI group for determination and approval of the best option, include a statement on the scope of the rule, as well as the resources required to complete it and an estimated timeline for implementation.Testing new rules. When deemed ready for implemen-tation, the rule is activated in background mode so that the rule is triggered according to the rule logic but no alert is presented to the prescriber. Rule activity is recorded and analyzed to ensure appropriate triggering of the rule. When testing, refinement, and retesting of the rule are completed, a foreground activation date is determined by the CI team, which is responsible for all EHR change man-agement. Educational bulletins are distributed to all EHR users one week prior to activation and again on the day of activation. Once activated, rule activity is monitored to validate the appropriateness of rule triggering and the associated pop-up alert.Example of rule development, implementation, and activity monitoring. A review of adverse-event and quality-measure compliance reports had identified treat-ment failures involving patients who received b-blockers prior to surgery but were not continued on these medica-tions after surgery. The corporate vice president of quality (VPQ) was the executive responsible for ensuring that our organization met Joint Commission and Centers for Medi-care and Medicaid Services National Hospital Inpatient Quality Measures Core Measures.2 The V PQ was interested in pursuing a CDS rule to help address compliance with the Surgical Care Improvement Project (SCIP) core mea-sure that addresses perioperative b-blocker administra-tion. The corporate vice president of clinical informat-ics was responsible for ensuring that our organization met the H ealth Information Technology for Economic and Clinical H ealth Act meaningful-use requirements. “Meaningful Use Stage 2” (MU2) requirements called for implementation of five CDS rules related to four or more core measures.3 During a CE division discussion, the VPQ and the VPCI agreed that a “SCIP-Card-2” b-blocker rule could have value in improving patient care while satisfy-ing core measure and meaningful-use requirements. A rule request form was initiated.SBAR information. The situation prompting the CDS rule request was the need to improve the ordering of perioperative b-blockers at our inpatient facilities. The background information consisted of documented re-cent failures to treat or to record valid reasons contrain-dicating b-blocker use that indicated a need to improve documentation and ordering of perioperative b-blockers to meet the SCIP-Card-2 core measure (the organization also needed to implement CDS rules addressing core measures in order to satisfy MU2 requirements). As-sessment information was obtained through a review of details of recent treatment and documentation failures; consideration of CDS tools indicated potential value in developing a rule to improve perioperative b-blocker ordering. Analysis of all this information led to a recom-mendation to pursue implementation of a rule to pro-mote perioperative b-blocker use.PARMI group identification.The identified process owners were the VPQ and the VPCI; the approvers were the quality directors and the hospital chief medical offi-cers; the resources and members were the EBM team and the ISD; the interested parties were the hospital quality departments and the medical, nursing, and pharmacy staffs.Rule design.The rule developed is triggered when a provider signs any EHR order.The rule logic first deter-mines if the patient’s status is postoperative day (POD) 0, 1, or 2; then it checks for notation of a b-blocker on the home medication list and, finally, an active inpatient b-blocker order. The alert triggers if the patient is POD 0, 1, or 2 and has a b-blocker on the home medication list but does not have an active inpatient b-blocker order. The prescriber is shown the date and time of surgery and details of the b-blocker order from the home medication list and given the opportunity to document the reason for not prescribing a b-blocker. If a b-blocker is indicated, the b-blocker medication order is placed after acknowl-edgment of the alert.Rule implementation.The PARMI group reviewed and approved the proposed rule trigger and logic. The ISD built the rule, and the EBM team tested the rule for proper triggering in background mode. After clinician training and notification, the rule was activated in the foreground. The EBM team monitored rule activity to confirm that the rule was triggering appropriately and that system response time had not been adversely affect-ed. The ISD help desk referred any clinician questions or comments regarding the new rule to the EBM team.Retrospective review.The EBM team conducted a ret-rospective chart review seven months after rule imple-mentation, and the review showed that the rule triggered CDS alerts on 105 patients. In response to 84 of those alerts, clinicians acknowledged and satisfied the SCIP-Card-2 measure by either ordering a b-blocker or docu-menting a reason why a b-blocker had not been admin-istered postoperatively, resulting in 100% SCIP-Card-2 compliance in terms of alert response. Alerts were not ac-knowledged in the remaining 21 cases; the chart reviewer discovered that in 18 of those 21 cases, the prescriber had independently ordered a b-blocker or documented a “nonadministration” reason outside of the rule alert-ing domain, resulting in 85% SCIP-Card-2 compliance in cases in which a CDS alert was neglected.Overall (i.e., systemwide) SCIP-Card-2 compliance had been 98.7% in the 6 months before implementation of the rule; in the period 6–12 months after implementa-tion, compliance improved to 99.1%. Although the over-all improvement in SCIP-Card-2 compliance was not sta-tistically significant, these findings supported the initial assessment that this rule could provide positive prescrib-ing guidance and help improve SCIP-Card-2 compliance. The PARMI group decided to keep the rule active to aid in the goal of reaching 100% compliance.1. Osheroff JA, Teich JA, Levick D et al. Improving outcomeswith clinical decision support: an implementer’s guide.2nd ed. Chicago: Healthcare Information and Management Systems Society; 2012:2.2. Agency for Healthcare Research and Quality. Set:Surgical Care Improvement Project (SCIP). www./browse/by-organization-indiv.aspx?orgid=22&objid=26093 (accessed 2014 Nov 21).3. Government Printing Office. Federal Register, Vol. 77, No.171, Tuesday, September 4, 2012, 42 CFR Parts 412, 413, and 495. /fdsys/pkg/FR-2012-09-04/pdf/2012-21050.pdf (accessed 2014 Nov 21).Armen I. Simonian, Pharm.D.Sharp HealthCareSan Diego, CA**********************Jason H. Lam, Pharm.D.Sharp HealthCareSan Diego, CAThe authors have declared no potential conflicts of interest.DOI 10.2146/ajhp150122。

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运筹学实验报告 2

运筹学实验报告学院：专业班级：姓名：学号：实验一线性规划一、实验目的学习WinQSB软件的基本操作，利用Linear Programming功能求解线性规划问题。

掌握线性规划的基本理论与求解方法，重点在于单纯形法的应用以及灵敏度分析方法。

二、实验内容安装WinQSB软件，了解WinQSB软件在Windows环境下的文件管理操作，熟悉软件界面内容，掌握操作命令。

利用Linear Programming功能建立线性模型，输入模型，求解模型，并对求解结果进行简单分析。

三、实验步骤1．将WinQSB文件复制到本地硬盘；在WinQSB文件夹中双击setup.exe。

2．指定安装WinQSB软件的目标目录（默认为C:\ WinQSB）。

3．安装过程需要输入用户名和单位名称（任意输入），安装完毕之后，WinQSB菜单自动生成在系统程序中。

4．熟悉WinQSB软件子菜单内容及其功能，掌握操作命令。

5．求解下面线性规划问题：某工厂要用三种原材料C、P、H混合调配出三种不同规格的产品A、B、D。

已知产品的规格要求，产品单价，每天能供应的原材料数量及原材料单价分别见下表1和2。

该厂应如何安排生产，使利润收入为最大？表1产品名称规格要求单价（元/kg）A 原材料C不少于50%原材料P不超过25%50B 原材料C不少于25%原材料P 不超过50%35D 不限25表2原材料名称每天最多供应量（kg）单价（元/kg）C P H 10010060652535列出该线性规划问题的模型如下：以A C 表示产品A 中C 的成分，A P 表示产品A 中P 的成分，依次类推。

则约束条件为：A C +BC +D C ≤100 A P +B P +D P ≤100 A H +B H +D H ≤60在约束条件中共有9个变量，为计算和叙述方便，分别用x 1,…,x 9表示。

令x 1=A c , x 2=A p , x 3=A H , x 4=B C , x 5=B P , x 6=B H , x 7=D C , x 8=D P , x 9=D H . 则：启动程序开始→程序→WinQSB →Linear and Integer Programming ，点击菜单栏File 中的New Problem 项，建立新问题。