2014全美数学建模MCM原文及翻译

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美国大学生数学建模比赛2014年B题

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Page 2 oon ............................................................................................................................................................. 3 2. The AHP .................................................................................................................................................................. 3 2.1 The hierarchical structure establishment ....................................................................................................... 4 2.2 Constructing the AHP pair-wise comparison matrix...................................................................................... 4 2.3 Calculate the eigenvalues and eigenvectors and check consistency .............................................................. 5 2.4 Calculate the combination weights vector ..................................................................................................... 6 3. Choosing Best All Time Baseball College Coach via AHP and Fuzzy Comprehensive Evaluation ....................... 6 3.1 Factor analysis and hierarchy relation construction....................................................................................... 7 3.2 Fuzzy comprehensive evaluation ................................................................................................................... 8 3.3 calculating the eigenvectors and eigenvalues ................................................................................................ 9 3.3.1 Construct the pair-wise comparison matrix ........................................................................................ 9 3.3.2 Construct the comparison matrix of the alternatives to the criteria hierarchy .................................. 10 3.4 Ranking the coaches .....................................................................................................................................11 4. Evaluate the performance of other two sports coaches, basketball and football.................................................... 13 5. Discuss the generality of the proposed method for Choosing Best All Time College Coach ................................ 14 6. The strengths and weaknesses of the proposed method to solve the problem ....................................................... 14 7. Conclusions ........................................................................................................................................................... 15

2014年美国大学生数学建模MCM-B题O奖论文

For ofﬁce use only T1T2T3T4T eam Control Number24857Problem ChosenBFor ofﬁce use onlyF1F2F3F42014Mathematical Contest in Modeling(MCM)Summary Sheet (Attach a copy of this page to each copy of your solution paper.)AbstractThe evaluation and selection of‘best all time college coach’is the prob-lem to be addressed.We capture the essential of an evaluation system by reducing the dimensions of the attributes by factor analysis.And we divide our modeling process into three phases:data collection,attribute clariﬁca-tion,factor model evaluation and model generalization.Firstly,we collect the data from ofﬁcial database.Then,two bottom lines are determined respectively by the number of participating games and win-loss percentage,with these bottom lines we anchor a pool with30to40 candidates,which greatly reduced data volume.And reasonably theﬁnal top5coaches should generate from this pool.Attribution clariﬁcation will be abundant in the body of the model,note that we endeavor to design an attribute to effectively evaluate the improvement of a team before and after the coach came.In phase three,we analyse the problem by following traditional method of the factor model.With three common factors indicating coaches’guiding competency,strength of guided team,competition strength,we get aﬁnal integrated score to evaluate coaches.And we also take into account the time line horizon in two aspects.On the one hand,the numbers of participating games are adjusted on the basis of time.On the other hand,we put forward a potential sub-model in our‘further attempts’concerning overlapping pe-riod of the time of two different coaches.What’s more,a‘pseudo-rose dia-gram’method is tried to show coaches’performance in different areas.Model generalization is examined by three different sports types,Foot-ball,Basketball,and Softball.Besides,our model also can be applied in all possible ball games under the frame of NCAA,assigning slight modiﬁcation according to speciﬁc regulations.The stability of our model is also tested by sensitivity analysis.Who’s who in College Coaching Legends—–A generalized Factor Analysis approach2Contents1Introduction41.1Restatement of the problem (4)1.2NCAA Background and its coaches (4)1.3Previous models (4)2Assumptions5 3Analysis of the Problem5 4Theﬁrst round of sample selection6 5Attributes for evaluating coaches86Factor analysis model106.1A brief introduction to factor analysis (10)6.2Steps of Factor analysis by SPSS (12)6.3Result of the model (14)7Model generalization15 8Sensitivity analysis189Strength and Weaknesses199.1Strengths (19)9.2Weaknesses (19)10Further attempts20 Appendices22 Appendix A An article for Sports Illustrated221Introduction1.1Restatement of the problemThe‘best all time college coach’is to be selected by Sports Illustrated,a magazine for sports enthusiasts.This is an open-ended problem—-no limitation in method of performance appraisal,gender,or sports types.The following research points should be noted:•whether the time line horizon that we use in our analysis make a difference;•the metrics for assessment are to be articulated;•discuss how the model can be applied in general across both genders and all possible sports;•we need to present our model’s Top5coaches in each of3different sports.1.2NCAA Background and its coachesNational Collegiate Athletic Association(NCAA),an association of1281institution-s,conferences,organizations,and individuals that organizes the athletic programs of many colleges and universities in the United States and Canada.1In our model,only coaches in NCAA are considered and ranked.So,why evaluate the Coaching performance?As the identity of a college football program is shaped by its head coach.Given their impacts,it’s no wonder high proﬁle athletic departments are shelling out millions of dollars per season for the services of coaches.Nick Saban’s2013total pay was$5,395,852and in the same year Coach K earned$7,233,976in total23.Indeed,every athletic director wants to hire the next legendary coach.1.3Previous modelsTraditionally,evaluation in athletics has been based on the single criterion of wins and losses.Years later,in order to reasonably evaluate coaches,many reseachers have implemented the coaching evaluation model.Such as7criteria proposed by Adams:[1] (1)the coach in the profession,(2)knowledge of and practice of medical aspects of coaching,(3)the coach as a person,(4)the coach as an organizer and administrator,(5) knowledge of the sport,(6)public relations,and(7)application of kinesiological and physiological principles.1Wikipedia:/wiki/National_Collegiate_Athletic_ Association#NCAA_sponsored_sports2USAToday:/sports/college/salaries/ncaaf/coach/ 3USAToday:/sports/college/salaries/ncaab/coach/Such models relatively focused more on some subjective and difﬁcult-to-quantify attributes to evaluate coaches,which is quite hard for sports fans to judge coaches. Therefore,we established an objective and quantiﬁed model to make a list of‘best all time college coach’.2Assumptions•The sample for our model is restricted within the scale of NCAA sports.That is to say,the coaches we discuss refers to those service for NCAA alone;•We do not take into account the talent born varying from one player to another, in this case,we mean the teams’wins or losses purely associate with the coach;•The difference of games between different Divisions in NCAA is ignored;•Take no account of the errors/amendments of the NCAA game records.3Analysis of the ProblemOur main goal is to build and analyze a mathematical model to choose the‘best all time college coach’for the previous century,i.e.from1913to2013.Objectively,it requires numerous attributes to judge and specify whether a coach is‘the best’,while many of the indicators are deemed hard to quantify.However,to put it in theﬁrst place, we consider a‘best coach’is,and supposed to be in line with several basic condition-s,which are the prerequisites.Those prerequisites incorporate attributes such as the number of games the coach has participated ever and the win-loss percentage of the total.For instance,under the conditions that either the number of participating games is below100,or the win-loss percentage is less than0.5,we assume this coach cannot be credited as the‘best’,ignoring his/her other facets.Therefore,an attempt was made to screen out the coaches we want,thus to narrow the range in ourﬁrst stage.At the very beginning,we ignore those whose guiding ses-sions or win-loss percentage is less than a certain level,and then we determine a can-didate pool for‘the best coach’of30-40in scale,according to merely two indicators—-participating games and win-loss percentage.It should be reasonably reliable to draw the top5best coaches from this candidate pool,regardless of any other aspects.One point worth mentioning is that,we take time line horizon as one of the inputs because the number of participating games is changing all the time in the previous century.Hence,it would be unfair to treat this problem by using absolute values, especially for those coaches who lived in the earlier ages when sports were less popular and games were sparse comparatively.4Theﬁrst round of sample selectionCollege Football is theﬁrst item in our research.We obtain data concerning all possible coaches since it was initiated,of which the coaches’tenures,participating games and win-loss percentage etc.are included.As a result,we get a sample of2053in scale.Theﬁrst10candidates’respective information is as below:Table1:Theﬁrst10candidates’information,here Pct means win-loss percentageCoach From To Years Games Wins Losses Ties PctEli Abbott19021902184400.5Earl Abell19281930328141220.536Earl Able1923192421810620.611 George Adams1890189233634200.944Hobbs Adams1940194632742120.185Steve Addazio20112013337201700.541Alex Agase1964197613135508320.378Phil Ahwesh19491949193600.333Jim Aiken19461950550282200.56Fred Akers19751990161861087530.589 ...........................Firstly,we employ Excel to rule out those who begun their coaching career earlier than1913.Next,considering the impact of time line horizon mentioned in the problem statement,we import our raw data into MATLAB,with an attempt to calculate the coaches’average games every year versus time,as delineated in the Figure1below.Figure1:Diagram of the coaches’average sessions every year versus time It can be drawn from theﬁgure above,clearly,that the number of each coach’s average games is related with the participating time.With the passing of time and the increasing popularity of sports,coaches’participating games yearly ascends from8to 12or so,that is,the maximum exceed the minimum for50%around.To further reﬁnethe evaluation method,we make the following adjustment for coaches’participating games,and we deﬁne it as each coach’s adjusted participating games.Gi =max(G i)G mi×G iWhere•G i is each coach’s participating games;•G im is the average participating games yearly in his/her career;and•max(G i)is the max value in previous century as coaches’average participating games yearlySubsequently,we output the adjusted data,and return it to the Excel table.Obviously,directly using all this data would cause our research a mass,and also the economy of description is hard to achieved.Logically,we propose to employ the following method to narrow the sample range.In general,the most essential attributes to evaluate a coach are his/her guiding ex-perience(which can be shown by participating games)and guiding results(shown by win-loss percentage).Fortunately,these two factors are the ones that can be quantiﬁed thus provide feasibility for our modeling.Based on our common sense and select-ed information from sports magazines and associated programs,weﬁnd the winning coaches almost all bear the same characteristics—-at high level in both the partici-pating games and the win-loss percentage.Thus we may arbitrarily enact two bottom line for these two essential attributes,so as to nail down a pool of30to40candidates. Those who do not meet our prerequisites should not be credited as the best in any case.Logically,we expect the model to yield insight into how bottom lines are deter-mined.The matter is,sports types are varying thus the corresponding features are dif-ferent.However,it should be reasonably reliable to the sports fans and commentators’perceptual intuition.Take football as an example,win-loss percentage that exceeds0.75 should be viewed as rather high,and college football coaches of all time who meet this standard are speciﬁcally listed in Wikipedia.4Consequently,we are able toﬁx upon a rational pool of candidate according to those enacted bottom lines and meanwhile, may tender the conditions according to the total scale of the coaches.Still we use Football to further articulate,to determine a pool of candidates for the best coaches,weﬁrst plot theﬁgure below to present the distributions of all the coaches.From theﬁgure2,weﬁnd that once the games number exceeds200or win-loss percentage exceeds0.7,the distribution of the coaches drops signiﬁcantly.We can thus view this group of coaches as outstanding comparatively,meeting the prerequisites to be the best coaches.4Wikipedia:/wiki/List_of_college_football_coaches_ with_a_.750_winning_percentageFigure2:Hist of the football coaches’number of games versus and average games every year versus games and win-loss percentageHence,we nail down the bottom lines for both the games number and the win-loss percentage,that is,0.7for the former and200for the latter.And these two bottom lines are used as the measure for ourﬁrst round selection.After round one,merely35 coaches are qualiﬁed to remain in the pool of candidates.Since it’s theﬁrst round sifting,rather than direct and ultimate determination,we hence believe the subjectivity to some extent in the opt of bottom lines will not cloud theﬁnal results of the best coaches.5Attributes for evaluating coachesThen anchored upon the35candidate selected,we will elaborate our coach evaluation system based on8attributes.In the indicator-select process,we endeavor to examine tradeoffs among the availability for data and difﬁculty for data quantiﬁcation.Coaches’pay,for example,though serves as the measure for coaching evaluation,the corre-sponding data are limited.Situations are similar for attributes such as the number of sportsmen the coach ever cultivated for the higher-level tournaments.Ultimately,we determine the8attributes shown in the table below:Further explanation:•Yrs:guiding years of a coach in his/her whole career•G’:Gi =max(G i)G mi×G i see it at last section•Pct:pct=wins+ties/2wins+losses+ties•SRS:a rating that takes into account average point differential and strength of schedule.The rating is denominated in points above/below average,where zeroTable2:symbols and attributessymbol attributeYrs yearsG’adjusted overall gamesPct win-lose percentageP’Adjusted percentage ratioSRS Simple Rating SystemSOS Strength of ScheduleBlp’adjusted Bowls participatedBlw’adjusted Bowls wonis the average.Note that,the bigger for this value,the stronger for the team performance.•SOS:a rating of strength of schedule.The rating is denominated in points above/below average,where zero is the average.Noted that the bigger for this value,the more powerful for the team’s rival,namely the competition is more ﬁerce.Sports-reference provides ofﬁcial statistics for SRS and SOS.5•P’is a new attribute designed in our model.It is the result of Win-loss in the coach’s whole career divided by the average of win-loss percentage(weighted by the number of games in different colleges the coach ever in).We bear in mind that the function of a great coach is not merely manifested in the pure win-loss percentage of the team,it is even more crucial to consider the improvement of the team’s win-loss record with the coach’s participation,or say,the gap between‘af-ter’and‘before’period of this team.(between‘after’and‘before’the dividing line is the day the coach take ofﬁce)It is because a coach who build a comparative-ly weak team into a much more competitive team would deﬁnitely receive more respect and honor from sports fans.To measure and specify this attribute,we col-lect the key ofﬁcial data from sports-reference,which included the independent win-loss percentage for each candidate and each college time when he/she was in the team and,the weighted average of all time win-loss percentage of all the college teams the coach ever in—-regardless of whether the coach is in the team or not.To articulate this attribute,here goes a simple physical example.Ike Armstrong (placedﬁrst when sorted by alphabetical order),of which the data can be ob-tained from website of sports-reference6.We can easily get the records we need, namely141wins,55losses,15ties,and0.704for win-losses percentage.Fur-ther,speciﬁc wins,losses,ties for the team he ever in(Utab college)can also be gained,respectively they are602,419,30,0.587.Consequently,the P’value of Ike Armstrong should be0.704/0.587=1.199,according to our deﬁnition.•Bowl games is a special event in theﬁeld of Football games.In North America,a bowl game is one of a number of post-season college football games that are5sports-reference:/cfb/coaches/6sports-reference:/cfb/coaches/ike-armstrong-1.htmlprimarily played by teams from the Division I Football Bowl Subdivision.The times for one coach to eparticipate Bowl games are important indicators to eval-uate a coach.However,noted that the total number of Bowl games held each year is changing from year to year,which should be taken into consideration in the model.Other sports events such as NCAA basketball tournament is also ex-panding.For this reason,it is irrational to use the absolute value of the times for entering the Bowl games (or NCAA basketball tournament etc.)and the times for winning as the evaluation measurement.Whereas the development history and regulations for different sports items vary from one to another (actually the differentiation can be fairly large),we here are incapable to ﬁnd a generalized method to eliminate this discrepancy ,instead,in-dependent method for each item provide a way out.Due to the time limitation for our research and the need of model generalization,we here only do root extract of blp and blw to debilitate the differentiation,i.e.Blp =√Blp Blw =√Blw For different sports items,we use the same attributes,except Blp’and Blw’,we may change it according to speciﬁc sports.For instance,we can use CREG (Number of regular season conference championship won)and FF (Number of NCAA Final Four appearance)to replace Blp and Blw in basketball games.With all the attributes determined,we organized data and show them in the table 3:In addition,before forward analysis there is a need to preprocess the data,owing to the diverse dimensions between these indicators.Methods for data preprocessing are a lot,here we adopt standard score (Z score)method.In statistics,the standard score is the (signed)number of standard deviations an observation or datum is above the mean.Thus,a positive standard score represents a datum above the mean,while a negative standard score represents a datum below the mean.It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.7The standard score of a raw score x is:z =x −µσIt is easy to complete this process by statistical software SPSS.6Factor analysis model 6.1A brief introduction to factor analysisFactor analysis is a statistical method used to describe variability among observed,correlated variables in terms of a potentially lower number of unobserved variables called factors.For example,it is possible that variations in four observed variables mainly reﬂect the variations in two unobserved variables.Factor analysis searches for 7Wikipedia:/wiki/Standard_scoreTable3:summarized data for best college football coaches’candidatesCoach From To Yrs G’Pct Blp’Blw’P’SRS SOS Ike Armstrong19251949252810.70411 1.199 4.15-4.18 Dana Bible19151946313860.7152 1.73 1.0789.88 1.48 Bernie Bierman19251950242780.71110 1.29514.36 6.29 Red Blaik19341958252940.75900 1.28213.57 2.34 Bobby Bowden19702009405230.74 5.74 4.69 1.10314.25 4.62 Frank Broyles19571976202570.7 3.162 1.18813.29 5.59 Bear Bryant19451982385080.78 5.39 3.87 1.1816.77 6.12 Fritz Crisler19301947182080.76811 1.08317.15 6.67 Bob Devaney19571972162080.806 3.16 2.65 1.25513.13 2.28 Dan Devine19551980222800.742 3.16 2.65 1.22613.61 4.69 Gilmour Dobie19161938222370.70900 1.27.66-2.09 Bobby Dodd19451966222960.713 3.613 1.18414.25 6.6 Vince Dooley19641988253250.715 4.47 2.83 1.09714.537.12 Gus Dorais19221942192320.71910 1.2296-3.21 Pat Dye19741992192400.707 3.16 2.65 1.1929.68 1.51 LaVell Edwards19722000293920.716 4.69 2.65 1.2437.66-0.66 Phillip Fulmer19922008172150.743 3.87 2.83 1.08313.42 4.95 Woody Hayes19511978283290.761 3.32 2.24 1.03117.418.09 Frank Kush19581979222710.764 2.65 2.45 1.238.21-2.07 John McKay19601975162070.7493 2.45 1.05817.298.59 Bob Neyland19261952212860.829 2.65 1.41 1.20815.53 3.17 Tom Osborne19731997253340.8365 3.46 1.18119.7 5.49 Ara Parseghian19561974192250.71 2.24 1.73 1.15317.228.86 Joe Paterno19662011465950.749 6.08 4.9 1.08914.01 5.01 Darrell Royal19541976232970.7494 2.83 1.08916.457.09 Nick Saban19902013182390.748 3.74 2.83 1.12313.41 3.86 Bo Schembechler19631989273460.775 4.12 2.24 1.10414.86 3.37 Francis Schmidt19221942212670.70800 1.1928.490.16 Steve Spurrier19872013243160.733 4.363 1.29313.53 4.64 Bob Stoops19992013152070.804 3.74 2.65 1.11716.66 4.74 Jock Sutherland19191938202550.81221 1.37613.88 1.68 Barry Switzer19731988162090.837 3.61 2.83 1.16320.08 6.63 John Vaught19471973253210.745 4.24 3.16 1.33814.7 5.26 Wallace Wade19231950243070.765 2.24 1.41 1.34913.53 3.15 Bud Wilkinson19471963172220.826 2.83 2.45 1.14717.54 4.94 such joint variations in response to unobserved latent variables.The observed vari-ables are modelled as linear combinations of the potential factors,plus‘error’terms. The information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a putationally this technique is equivalent to low rank approximation of the matrix of observed variables.8 Why carry out factor analyses?If we can summarise a multitude of measure-8Wikipedia:/wiki/Factor_analysisments with a smaller number of factors without losing too much information,we have achieved some economy of description,which is one of the goals of scientiﬁc investi-gation.It is also possible that factor analysis will allow us to test theories involving variables which are hard to measure directly.Finally,at a more prosaic level,factor analysis can help us establish that sets of questionnaire items(observed variables)are in fact all measuring the same underlying factor(perhaps with varying reliability)and so can be combined to form a more reliable measure of that factor.6.2Steps of Factor analysis by SPSSFirst we import the decided datasets of8attributes into SPSS,and the results can be obtained below after the software processing.[2-3]Figure3:Table of total variance explainedFigure4:Scree PlotTheﬁrst table and scree plot shows the eigenvalues and the amount of variance explained by each successive factor.The remaining5factors have small eigenvalues value.Once the top3factors are extracted,it adds up to84.3%,meaning a great as the explanatory ability for the original information.To reﬂect the quantitative analysis of the model,we obtain the following factor loading matrix,actually the loadings are in corresponding to the weight(α1,α2 (i)the set ofx i=αi1f1+αi2f2+...+αim f j+εiAnd the relative strength of the common factors and the original attribute can also be manifested.Figure5:Rotated Component MatrixThen,with Rotated Component Matrix above,weﬁnd the common factor F1main-ly expresses four attributes they are:G,Yrs,P,SRS,and logically,we deﬁne the com-mon factor generated from those four attributes as the guiding competency of the coach;similarly,the common factor F2mainly expresses two attributes,and they are: Pct and Blp,which can be de deﬁned as the integrated strength of the guided team; while the common factor F3,mainly expresses two attributes:SOS and Blw,which can be summarized into a‘latent attribute’named competition strength.In order to obtain the quantitative relation,we get the following Component Score Coefﬁcient Matrix processed by SPSS.Further,the function of common factors and the original attributes is listed as bel-low:F1=0.300x1+0.312x2+0.023x3+0.256x4+0.251x5+0.060x6−0.035x7−0.053x8F2=−0.107x1−0,054x2+0.572x3+0.103x4+0.081x5+0.280x6+0.372x7+0.142x8 F3=−0.076x1−0,098x2−0.349x3+0.004x4+0.027x5−0.656x6+0.160x7+0.400x8 Finally we calculate out the integrated factor scores,which should be the average score weighted by the corresponding proportion of variance contribution of each com-mon factor in the total variance contribution.And the function set should be:F=0.477F1+0.284F2+0.239F3Figure6:Component Score Coefﬁcient Matrix6.3Result of the modelwe rank all the coaches in the candidate pool by integrated score represented by F.Seetable4:Table4:Integrated scores for best college football coach(show15data due to the limi-tation of space)Rank coaches F1F2F3Integrated factor1Joe Paterno 3.178-0.3150.421 1.3622Bobby Bowden 2.51-0.2810.502 1.1113Bear Bryant 2.1420.718-0.142 1.0994Tom Osborne0.623 1.969-0.2390.8205Woody Hayes0.140.009 1.6130.4846Barry Switzer-0.705 2.0360.2470.4037Darrell Royal0.0460.161 1.2680.4018Vince Dooley0.361-0.442 1.3730.3749Bo Schembechler0.4810.1430.3040.32910John Vaught0.6060.748-0.870.26511Steve Spurrier0.5180.326-0.5380.18212Bob Stoops-0.718 1.0850.5230.17113Bud Wilkinson-0.718 1.4130.1050.16514Bobby Dodd0.08-0.2080.7390.16215John McKay-0.9620.228 1.870.151Based on this model,we can make a scientiﬁc rank list for US college football coach-es,the Top5coaches of our model is Joe Paterno,Bobby Bowden,Bear Bryant,TomOsborne,Woody Hayes.In order to conﬁrm our result,we get a ofﬁcial list of bestcollege football coaches from Bleacherreport99Bleacherreport:/articles/890705-college-football-the-top-50-coTable5:The result of our model in football,the last column is ofﬁcial college basketball ranking from bleacherreportRank Our model Integrated scores bleacherreport1Joe Paterno 1.362Bear Bryant2Bobby Bowden 1.111Knute Rockne3Bear Bryant 1.099Tom Osborne4Tom Osborne0.820Joe Paterno5Woody Hayes0.484Bobby Bowden By comparing thoes two ranking list,weﬁnd that four of our Top5coaches ap-peared in the ofﬁcal Top5list,which shows that our model is reasonable and effective.7Model generalizationOur coach evaluation system model,of which the feasibility of generalization is sat-isfying,can be accommodated to any possible NCAA sports concourses by assigning slight modiﬁcation concerning speciﬁc regulations.Besides,this method has nothing to do with the coach’s gender,or say,both male and female coaches can be rationally evaluated by this system.And therefore we would like to generalize this model into softball.Further,we take into account the time line horizon,making corresponding adjust-ment for the indicator of number of participating games so as to stipulate that the evaluation measure for1913and2013would be the same.To further generalize the model,ﬁrst let’s have a test in basketball,of which the data available is adequate enough as football.And the speciﬁc steps are as following:1.Obtain data from sports-reference10and rule out the coaches who begun theircoaching career earlier than1913.2.Calculate each coach’s adjusted number of participating games,and adjust theattribute—-FF(Number of NCAA Final Four appearance).3.Determine the bottom lines for theﬁrst round selection to get a pool of candidatesaccording to the coaches’participating games and win-loss percentage,and the ideal volumn of the pool should be from30to40.Hist diagrams are as below: We determine800as the bottom line for the adjusted participating games and0.7 for the win-loss percentage.Coincidently,we get a candidate pool of35in scale.4.Next,we collect the corresponding data of candidate coaches(P’,SRS,SOS etc.),as presented in the table6:5.Processed by z score method and factor analysis based on the8attributes anddata above,we get three common factors andﬁnal integrated scores.And among 10sports-reference:/cbb/coaches/Figure7:Hist of the basketball coaches’number of games versus and average gamesevery year versus games and win-loss percentagethe top5candidates,Mike Krzyzewski,Adolph Rupp,Dean SmithˇcˇnBob Knightare the same with the ofﬁcial statistics from bleacherreport.11We can say theeffectiveness of the model is pretty good.See table5.We also apply similar approach into college softball.Maybe it is because the popularity of the softball is not that high,the data avail-able is not adequate to employ ourﬁrst model.How can our model function in suchsituation?First and foremost,specialized magazines like Sports Illustrated,its com-mentators there would have more internal and conﬁdential databases,which are notexposed publicly.On the one hand,as long as the data is adequate enough,we can saythe original model is completely feasible.While under the situation that there is datadeﬁcit,we can reasonably simplify the model.The derivation of the softball data is NCAA’s ofﬁcial websites,here we only extractdata from All-Division part.12Softball is a comparatively young sports,hence we may arbitrarily neglect the re-stricted condition of‘100years’.Subsequently,because of the data deﬁcit it is hard toadjust the number of participating games.We may as well determine10as the bottomline for participating games and0.74for win-loss percentage,producing a candidatepool of33in scaleAttributed to the inadequacy of the data for attributes,it is not convenient to furtheruse the factor analysis similarly as the assessment model.Therefore,here we employsolely two of the most important attributes to evaluate a coach and they are:partic-ipating games and win-loss percentage in the coach’s whole career.Speciﬁcally,weﬁrst adopt z score to normalize all the data because of the differentiation of various dimensions,and then the integrated score of the coach can be reached by the weighted11bleacherreport:/articles/1341064-10-greatest-coaches-in-ncaa-b 12NCAA softball Coaching Record:/Docs/stats/SB_Records/2012/coaches.pdf。

2014年美国大学生数学建模竞赛MCM A题二等奖

For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________
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Simulations of a Multi-Lane Traffic Model Using Cellular Automata Concerning the Overtaking Effect
Summary
The prosperity of modern industrialized world is largely depend on today’s sophisticated road networks. The rapid growth of vehicle number often exceeds the capacity of existing road [1,2]. Thus the effective utilization of road capacity is indispensable in traffic flow control. Cellular automaton model (CA model) is an very practical model in stimulating traffic flow behavior. This paper aims at building a CA model for multi-lane traffic using right-most overtaking law. The first CA model is the well-known NaSch model[9] Knospe studied a two-lane model focus on the density dependence of lane changes[10,11]. A numerical approach is performed by Daoudia and Moussa to stimulate the 3-lane traffic flow[12]. Basing upon the previous done by [1,9,10,12], we put forward an extended CA model using right-most overtaking rule. By a detailed investigation on overtaking process, we obtain the least safe distance under different speed limits and traffic flow densities, due to the limitation of least safe distance, we put forward incentive and safety criteria of overtaking behavior for particles on different lanes in our CA model. Simulation of our model is performed for three-lane case, and the result shows that our right-most overtaking rule behaves asymmetrically such that the right-most lane firstly reach at the “critical density” where the traffic flow reaches its peak point. And despite the special behavior of our own model, our results indicate a robust behavior of traffic flow such that when traffic density is roughly 0.1, the traffic flow arrives at its peak value, and with an increase of particle density, the phase transition occurs such that the traffic jams and “stop-and-go” phenomena happens. This result is of significance in conducting the daily traffic flow in our real world. Keywords: traffic flow, cellular automaton, right-most overtaking, simulation

数模美国赛总结部分英文

数模美国赛总结部分英文第一篇：数模美国赛总结部分英文Conclusions1、As our team set out to come up with a strategy on what would be the most efficient way to 我们提出了一种最有效的方法去解决……2、The first aspect that we took into major consideration was…….Other important findings through research made it apparent that the standard 首先我们考虑到……，其他重要的是我们通过研究使4、We have used mathematical modeling in a……to analyze some of the factors associated with such an activity。

为了分析这类问题的一些因素，我们运用数学模型……5、This “cannon problem” has been used in many forms in many differential equations courses in the Department of Mathematical Sciences for several years.这些年这些问题已经以不同的微分方程形式运用于自然科学部门。

6、In conclusion our team is very certain that the methods we came up with in 总之，我们很确定我们提出的方法7、We already know how well our results worked for…… 我们已经知道我们结果对……8、Now that the problem areas have been defined, we offer some ways to reduce the effect of these problems.既然已经定义了结果，我们提出一些方法减少对问题的影响。

2014数学中国MCMICM参赛指南翻译

数学中国MCM/ICM参赛指南翻译（2014版）（任何单位转载须注明来源：）MCM:The Mathematical Contest in ModelingMCM：数学建模竞赛ICM:TheInterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCMcontests,except where otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsoredby a faculty advisor fromits institution.每个MCM的参赛队需有一名所在单位的指导教师负责。

Team Advisors: Please read these instructions carefully. It is yourresponsibility to make sure that teams are correctly registered and that all ofthe following steps required for participation in the contest are completed:Please print a copy of these contest instructions forreference before, during, and after the contest. Clickhere for the printer friendly version.指导老师：请认真阅读这些说明，确保完成了所有相关的步骤。

2014MCM-B优秀论文

2014MCM-B-优秀论文美赛丛书目录（考虑）1. 问题2. 问题背景与问题分析3. 评价指标体系选哪些指标？理由何在？如何度量？4. 排名模型（权重模型）5. 时间因素处理6. 模型检验7. 问题综合分析与进一步研究8. 优秀论文A-26911-东南大学9. 优秀论文B - 30680-美国-北卡26160-重庆大学摘要：灰色与模糊评价模型，另外考虑了性别与时间因素。

AHP筛选特征因子，7个因子，灰色相关模型，模糊综合评价模型，灰色模型略强，时间因素对前十人选影响较小。

26160-重庆大学.pdf评价：除结果图外，乏善可陈，时间因素影响的结论有误。

26636-外经贸大学摘要：灰色相关模型，依据专家意见选择了四个评价指标：NCAA冠军，Pct，胜场数，教练报酬。

模糊相容矩阵确定各个评价指标的权值，结果与ESPN作比较。

最后讨论了时间因素，发现规律：“从前”的教练的胜率要远远高于“现在”的教练，但其他三个指标所受到的影响很小。

引入滑动平均方法，将时间因素纳入胜率计算模型中，这是本文的一个亮点。

Shannon熵用于评价稳定性。

讨论了参数敏感性。

便利与普适是我们模型的最大优点，但存在指标选择的主观性。

26636-外经贸.pdf评价：指标体系以及评价模型一般，有点投机，时间因素讨论、模型结果检验以及敏感性检验是亮点，结果对比表达清晰明了，可信度高。

缺假设与“conclusion”，是硬伤。

26911-东南大学三阶段全面评价模型，指标体系（胜率，稳定性，获得冠军数量，个人报酬，点击率，个人荣誉，职业联赛排名），谷歌趋势统计方法，线性拟合方法，加权和模型，AHP+最大熵模型，灰色相关分析，综合排名26911-东南大学.pdf评价：非常全面，思路很清晰，表达很简洁，值得效仿。

具体说：指标意义讨论充分；指标取值实用、合理；时间因素考虑到位；权重确定有技术含量；结果表达清晰；文章节奏把握好。

如果按更高标准衡量，第二种权重体系中GRA的作用不大显著。

HIMCM 2014美国中学生数学建模竞赛试题

HIMCM 2014美国中学生数学建模竞赛试题Problem A: Unloading Commuter TrainsTrains arrive often at a central Station, the nexus for many commuter trains from suburbs of larger cities on a “commuter” line. Most trains are long (perhaps 10 or more cars long). The distance a passenger has to walk to exit the train area is quite long. Each train car has only two exits, one near each end so that the cars can carry as many people as possible. Each train car has a center aisle and there are two seats on one side and three seats on the other for each row of seats.To exit a typical station of interest, passengers must exit the car, and then make their way to a stairway to get to the next level to exit the station. Usually these trains are crowded so there is a “fan” of passengers from the train trying to get up the stairway. The stairway could accommodate two columns of people exiting to the top of the stairs.Most commuter train platforms have two tracks adjacent to the platform. In the worst case, if two fully occupied trains arrived at the same time, it might take a long time for all the passengers to get up to the main level of the station.Build a mathematical model to estimate the amount of time for a passenger to reach the street level of the station to exit the complex. Assume there are n cars to a train, each car has length d. The length of the platform is p, and the number of stairs in each staircase is q. Use your model to specifically optimize (minimize) the time traveled to reach street level to exit a station for the following:问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。

2014美国数学建模竞赛赛题翻译

问题A：右行左超规则在美国、中国和大多数除了英国、澳大利亚和一些前英国殖民地的国家，多车道高速公路常常有这样一种规则。

司机必须尽量在最右的车道行使，只有超车时，司机才可以向左移动一个车道来达成目的。

当司机超车完毕后必须回到原车道继续行使。

建立并分析一个数学模型，使得这个模型能够分析这个规则在交通高负荷和低负荷情况下的表现。

你可以从许多角度来思考这个问题，比如车流量和车辆安全之间的权衡，或者一个过快或过慢的车辆限速带来的影响等等。

这个规则可以使我们获得更好的交通流？如果不可以，请提出并分析一个替代方案使得交通流得到优化、安全得到保障、或者其他你认为重要的因素得到实现。

在靠左行使才是规则的国家，论证你的解决方案是否可以通过简单的变换或者通过增加一些新的要求来解决相同的问题。

最后，以上的规则的实行是建立在人们遵守它的基础上的，然而不是所有人都愿意去遵守。

那么现在我们使同一条道（可以只是一段，也可以是全段公路）上的交通车辆都在一个智能系统的严格控制下，这个变化对你之前的分析结果有多大的影响？问题B：体育画刊是一个为体育爱好者们设计的杂志。

这个杂志正在寻找上世纪女性或者男性的“历来最优秀的大学教练”。

建立一个数学模型，从男性或者女性体育教练中选择最好的大学教练（退役或者在役的都可以）。

这些体育教练可以是大学曲棍球、陆上曲棍球、足球、橄榄球、棒球、排球、篮球的教练。

你选择划分的时间会对你的分析有影响吗？也就是说，1913年的教练方式和2013年的会有什么不同吗？清楚的阐述你的评估方式。

讨论你的模型如何通用于两性教练和所有可能的运动项目上。

用你的模型为三项体育项目分别找到五个最佳教练。

再为体育画刊提供一篇1－2页的不涉及技术性问题解释的通俗易懂的文章来解释你们的结果，你们必须保证体育爱好者们能够理解。

【VIP专享】2010 -2014MCM Problems建模竞赛美赛题目中英文双语翻译版

2010 MCM ProblemsPROBLEM A: The Sweet SpotExplain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?MCM 2010 A题：解释棒球棒上的“最佳击球点”每一个棒球手都知道在棒球棒比较粗的部分有一个击球点，这里可以把打击球的力量最大程度地转移到球上。

2014美国数学建模竞赛 C题论文【COMAP 31223】

Team # 31223
Page 2 of 19
Contents
1. Introduction 2. Model 2.1Properties of a Successful Model 2.2Assumption 2.3Build Evaluating igist of scoring training ability 2.4.2 the process of scoring training ability 2.5.1 Set the personal quality and management capability system 2.5.2 Build Hierarchical levels 2.5.3build judgment matrix 3.1 the best basketball coach 3.1.1 The Filtering Model 3.1.2 The AHP Model 3.1.3 Consistency Test 3.2the best football coach 3.3the best hockey coach 4. Conclusions 5. Adaptability of the model 5.1 Applicability of the time 5.2 Applicability of the different sports 6.Sensitivity Test 7. Assessment 8. References 9.Advertising shee
Abstract
Considering the coach and the player final destination is to win the games, so we choose the coach’s training ability into our indexes evaluation system. Like that, we continue choose the personal quality and management capability into our indexes evaluation system. Then Among these indexes, we take training ability as the key index. Only the coaches who rank top ten are certificated to enter the next evaluating system, that is the AHP model. Next, the AHP model takes training ability, personal quality and management capability as criteria. So we can find the highest weight coach. In the application of basketball, first, we use the data of win-loss percentage, Conference Champion, NCAA Final Fours and NCAA Championship to measure on the training ability. Then choose 10 coaches from 3513 ones. Then, we make a list of the length of coaching career, life major events, major honors and awards to determine their personal qualities. What is more, to objectively measure the priorities, we apply average weighted sum, Wilcox Rank method to the normalized data. Finally, we obtain the final weights of the 10 coaches. It is shown that the top 5 coaches are John Wooden, Dean Smith，Mike Krzyzewski，Rick Pitino and Roy Williams. In our model, it contains various information of the coach, like whether he has some good or bad behavior, how much is the team improved under the guidance of the coach. So the model can comprehensive evaluation a coach. To test the applicability of the model, we collect 2051 and 351 samples from the internet, and find that the model’s evaluation system can be widely applied to other sports. Through comparison and analysis, we find that although training ability is very important when evaluating coaches, other indexes matters too. For example, Rick Pitino ranks fifth in the end, but his training ability ranks out of top 5. It is his significant management improves his final rank. We adopt Wilcox Rank Test in time horizon problem. Then, the significance level is less than 0.05. So we carefully compare the data and information classified by time. It comes out that more and more regular seasons are held accordingly. But our model does not consider the factor.

2014美国数学建模竞赛 MCM A题参考答案元胞自动机

clfclear all%build the GUI%define the plot buttonplotbutton=uicontrol('style','pushbutton',...'string','Run', ...'fontsize',12, ...'position',[100,400,50,20], ...'callback', 'run=1;');%define the stop buttonerasebutton=uicontrol('style','pushbutton',...'string','Stop', ...'fontsize',12, ...'position',[200,400,50,20], ...'callback','freeze=1;');%define the Quit buttonquitbutton=uicontrol('style','pushbutton',...'string','Quit', ...'fontsize',12, ...'position',[300,400,50,20], ...'callback','stop=1;close;');number = uicontrol('style','text', ...'string','1', ...'fontsize',12, ...'position',[20,400,50,20]);%CA setupn=100;%数据初始化z=zeros(1,n);%元胞个数z=roadstart(z,5);%道路状态初始化，路段上随机分布5辆cells=z;vmax=3;%最大速度v=speedstart(cells,vmax);%速度初始化x=1;%记录速度和车辆位置memor_cells=zeros(3600,n);memor_v=zeros(3600,n);imh=imshow(cells);%初始化图像白色有车，黑色空元胞set(imh, 'erasemode', 'none')axis equalaxis tightstop=0; %wait for a quit button pushrun=0; %wait for a drawfreeze=0; %wait for a freeze（冻结）while (stop==0)if(run==1)%边界条件处理，搜素首末车，控制进出，使用开口条件a=searchleadcar(cells);b=searchlastcar(cells);[cells,v]=border_control(cells,a,b,v,vmax); i=searchleadcar(cells);%搜索首车位置for j=1:iif i-j+1==n[z,v]=leadcarupdate(z,v);continue;else%======================================加速、减速、随机慢化 if cells(i-j+1)==0;%判断当前位置是否非空continue;else v(i-j+1)=min(v(i-j+1)+1,vmax);%加速%=================================减速k=searchfrontcar((i-j+1),cells);%搜素前方首个非空元胞位置if k==0;%确定于前车之间的元胞数d=n-(i-j+1);else d=k-(i-j+1)-1;endv(i-j+1)=min(v(i-j+1),d);%==============================%减速%随机慢化v(i-j+1)=randslow(v(i-j+1));new_v=v(i-j+1);%======================================加速、减速、随机慢化%更新车辆位置z(i-j+1)=0;z(i-j+1+new_v)=1;%更新速度v(i-j+1)=0;v(i-j+1+new_v)=new_v;endendendcells=z;memor_cells(x,:)=cells;%记录速度和车辆位置memor_v(x,:)=v;x=x+1;set(imh,'cdata',cells)%更新图像%update the step number diaplaypause(0.2);stepnumber = 1 + str2num(get(number,'string'));set(number,'string',num2str(stepnumber))endif (freeze==1)run = 0;freeze = 0;enddrawnowend///////////////////////////////////////////////////////////////////////Function[new_matrix_cells,new_v]=border_control(matrix_cells,a,b,v,vmax) %边界条件，开口边界，控制车辆出入%出口边界，若头车在道路边界，则以一定该路0.9离去n=length(matrix_cells);if a==nrand('state',sum(100*clock)*rand(1));%¶¨ÒåËæ»úÖÖ×Óp_1=rand(1);%产生随机概率if p_1<=1 %如果随机概率小于0.9，则车辆离开路段，否则不离口matrix_cells(n)=0;v(n)=0;endend%入口边界，泊松分布到达，1s内平均到达车辆数为q，t为1sif b>vmaxt=1;q=0.25;x=1;p=(q*t)^x*exp(-q*t)/prod(x);%1s内有1辆车到达的概率rand('state',sum(100*clock)*rand(1));p_2=rand(1);if p_2<=pm=min(b-vmax,vmax);matrix_cells(m)=1;v(m)=m;endendnew_matrix_cells=matrix_cells;new_v=v;///////////////////////////////////////////////////////////////////////function [new_matrix_cells,new_v]=leadcarupdate(matrix_cells,v)%第一辆车更新规则n=length(matrix_cells);if v(n)~=0matrix_cells(n)=0;v(n)=0;endnew_matrix_cells=matrix_cells;new_v=v;///////////////////////////////////////////////////////////////////////function [new_v]=randslow(v)p=0.3;%慢化概率rand('state',sum(100*clock)*rand(1));%¶¨ÒåËæ»úÖÖ×Óp_rand=rand;%产生随机概率if p_rand<=pv=max(v-1,0);endnew_v=v;///////////////////////////////////////////////////////////////////////function [matrix_cells_start]=roadstart(matrix_cells,n)%道路上的车辆初始化状态，元胞矩阵随机为0或1，matrix_cells初始矩阵，n初始车辆数k=length(matrix_cells);z=round(k*rand(1,n));for i=1:nj=z(i);if j==0matrix_cells(j)=0;elsematrix_cells(j)=1;endendmatrix_cells_start=matrix_cells;///////////////////////////////////////////////////////////////////////function[location_frontcar]=searchfrontcar(current_location,matrix_cells)i=length(matrix_cells);if current_location==ilocation_frontcar=0;elsefor j=current_location+1:iif matrix_cells(j)~=0location_frontcar=j;break;elselocation_frontcar=0;endendend///////////////////////////////////////////////////////////////////////function [location_lastcar]=searchlastcar(matrix_cells)%搜索尾车位置for i=1:length(matrix_cells)if matrix_cells(i)~=0location_lastcar=i;break;else %如果路上无车，则空元胞数设定为道路长度location_lastcar=length(matrix_cells);endend///////////////////////////////////////////////////////////////////////function [location_leadcar]=searchleadcar(matrix_cells)i=length(matrix_cells);for j=1:iif matrix_cells(i-j+1)~=0location_leadcar=i-j+1;break;elselocation_leadcar=0;endend///////////////////////////////////////////////////////////////////////function [v_matixcells]=speedstart(matrix_cells,vmax)%道路初始状态车辆速度初始化v_matixcells=zeros(1,length(matrix_cells));for i=1:length(matrix_cells)if matrix_cells(i)~=0v_matixcells(i)=round(vmax*rand(1));endend。

2014年美国大学生数学建模竞赛ICM(C题)一等奖

2 Assumptions
All the data given and found is valid and believable We don’t take the people with Erdos number>1 or Erdos number=0 (being Erdos himself) into account. The timeline of cooperation can be neglected. Neglecting the isolated node does not influence the accurate result.
Team # 25072Байду номын сангаас
Page 1 of 20
1 Introduction
Network science is an interdisciplinary academic field which studies complex networks [1]. One of the techniques to determine influence of academic research is to build a citation or co-author networks and analyze its properties. Erdos is the most famous academic co-authors on account of his over 500 co-author and over 1400 papers published. So it is of great significance to analyze the co-author data within Erdos1. How to build the co-author network and develop influence measures to determine the most influential one? It requires us some skills for data extraction in order to remove the invalid data and limit the size of the network that we are going to research. Also, ability to analyze the properties of the network is needed so as to figure out the feature of the network. On one hand our goal is to establish a mathematics model to determine the most significant author. There is no need to consider Erdos since he will link to all nodes in Erdos1. On the other hand we are required to develop another different model to determine the most important works. Moreover, we will implement our algorithm on a completely different set of network influence data –for instance, influential songwriters, music bands, performers, movie actors, directors, movies, TV shows, columnists, journalists, newspapers, magazines, novelists, novels, bloggers, tweeters and so on. Finally, we will discuss the science, understanding and utility of modeling influence and impact within networks and draw some conclusion. What’s more, we can also try to apply our model to the network of university, department, nation and society to demonstrate our models have good practicability and adaptability.

2014年数学建模美赛题目原文及翻译

2014年数学建模美赛题目原文及翻译作者：Ternence Zhang转载注明出处：MCM原题PDF：PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this ruleeffective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system –either part of the road network or imbedded in the design of all vehicles using the roadway –to what extent would this change the results of your earlier analysis?问题A：车辆右行在一些规定汽车靠右行驶的国家（即美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地），多车道的高速公路经常使用这样一条规则：要求司机开车时在最右侧车道行驶，除了在超车的情况下，他们应移动到左侧相邻的车道，超车，然后恢复到原来的行驶车道（即最右车道）。

2014美国大学生数学建模特等奖优秀论文

Team#31552
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Best all time college coach Summary
In order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical Hierarchy Process. The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly ， Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the selecting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball composite score, namely the order of male basketball coaches, which is shown in Table 7. Adolph Rupp and Mark Few are the last century and this century's "best all time college coach" respectively. It is realistic. The rank of college coaches can be clearly determined through this method. Next, ANOVA shows that the scores of last century’s coaches and this century’s coaches have significant difference, which demonstrates that time line horizon exerts influence upon the evaluation and gender factor has no significant influence on coaches’ score. The assessment model, therefore, can be applied to both male and female coaches. Nevertheless, based on this, we have drawn coaches’ coaching ability distributing diagram under ideal situation and non-ideal situation according to the data we have found, through which we get that if time line horizon is chosen reasonably, it will not affect the selecting results. In this problem, the time line horizon of the year 2000 will not influence the selecting results. Furthermore, we put the data of the three types of sports, which have been found by us, into the above Model, and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table12 and Table13 respectively. These results are compared with the results on the Internet[7], so as to examine the reasonableness of our results. We choose the sports randomly which undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model. Finally, we have prepared a 1-2 page article for Sports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans will understand. Key words: TOPSIS Improved Model; Entropy; Analytical Hierarchy Process; Comprehensive Evaluation Model; ANOVA

美国大学生数学建模竞赛优秀论文翻译

优化和评价的收费亭的数量景区简介由於公路出来的第一千九百三十，至今发展十分迅速在全世界逐渐成为骨架的运输系统，以其高速度，承载能力大，运输成本低，具有吸引力的旅游方便，减少交通堵塞。

以下的快速传播的公路，相应的管理收费站设置支付和公路条件的改善公路和收费广场。

然而，随着越来越多的人口密度和产业基地，公路如花园州公园大道的经验严重交通挤塞收费广场在高峰时间。

事实上，这是共同经历长时间的延误甚至在非赶这两小时收费广场。

在进入收费广场的车流量，球迷的较大的收费亭的数量，而当离开收费广场，川流不息的车辆需挤缩到的车道数的数量相等的车道收费广场前。

因此，当交通繁忙时，拥堵现象发生在从收费广场。

当交通非常拥挤，阻塞也会在进入收费广场因为所需要的时间为每个车辆付通行费。

因此，这是可取的，以尽量减少车辆烦恼限制数额收费广场引起的交通混乱。

良好的设计，这些系统可以产生重大影响的有效利用的基础设施，并有助于提高居民的生活水平。

通常，一个更大的收费亭的数量提供的数量比进入收费广场的道路。

事实上，高速公路收费广场和停车场出入口广场构成了一个独特的类型的运输系统，需要具体分析时，试图了解他们的工作和他们之间的互动与其他巷道组成部分。

一方面，这些设施是一个最有效的手段收集用户收费或者停车服务或对道路，桥梁，隧道。

另一方面，收费广场产生不利影响的吞吐量或设施的服务能力。

收费广场的不利影响是特别明显时，通常是重交通。

其目标模式是保证收费广场可以处理交通流没有任何问题。

车辆安全通行费广场也是一个重要的问题，如无障碍的收费广场。

封锁交通流应尽量避免。

模型的目标是确定最优的收费亭的数量的基础上进行合理的优化准则。

主要原因是拥挤的随着经济的发展，交通系统逐渐形成和完善自己。

不同种类的车辆已迅速改善的数量，质量，速度，和类型。

为了支付维修费用的高速公路，收费站系统的建立。

然而，费时费给我们带来的拥塞，高度增加烦恼的司机。

一般来说，在收费亭的数量大于数量的车道。