ch05

Instructor’sManualChapter545ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.Chapter5IChapterOutline5.1ASimpleProblem:OperationsatConleyFisheries5.2PreliminaryAnalysisofConleyFisheries5.3ASimulationModeloftheConleyFisheriesProblem5.4RandomNumberGeneratorsDefinitionofarandomnumbergenerator.DiscussionontheExcelfunctionRAND(),usedtogeneraterandomnumbers.5.5CreatingNumbersthatobeyaDiscreteProbabilityDistributionAgeneralmethodtogeneraterandomnumbersobeyingagivendiscreteprobabilitydistributionispresented.5.6CreatingNumbersthatobeyaContinuousProbabilityDistributionDiscussiononhowtousetheinversefunctionofthecumulativedistributionofacontinuousrandomvariabletogeneraterandomnumbersaccordingtosuchdistribution.5.7CompletingtheSimulationModelofConleyFisheries5.8UsingtheSampleDataforAnalysisUsingtheConleyFisheriesexample,theauthorsshow,basedontheresultsofasimulation,howtoestimatetheprobabilitydistribution,average,standarddeviation,andrelatedstatisticsofagivenrandomvariable.5.9SummaryofSimulationModeling,andGuidelinesontheUseofSimulation5.10ComputerSoftwareforSimulationModeling5.11TypicalUseofSimulationModelsIITeachingTips1.Todevelopintuitionwithrespecttorandomnumbergenerationamongyourstudents,trycreatingasimulationoftheresultoftossingacoinandtheresultfromthrowingadieinclass.Engagingyourstudentsinasimulatedcasinogamecanenhancethisexperience.Instructor’sManualChapter546ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.2.Toreinforcetheconceptofsimulation,youmaywanttocontrastthesimulationapproachtootherscenarioanalysistechniquessuchasbest-case-worst-casescenarioanalysisorwhat-ifscenarioanalysis.Inparticular,byshowingseveralprobabilitydistributions,notnecessarilybellshaped,youcanexplainwhythebest-case-worst-caseanalysissometimesfailstoprovideagoodanswer.Also,youcanarguethatsimulationislikeanautomatedwhat-ifanalysis.IIIAnswerstoChapterCasesTHEGENTLELENTILRESTAURANTLetNbethenumberofmealssoldpermonth,Pthepriceofaprixfixemeal,andLthemonthlylaborcosts.ThenSanjay'smonthlysalarywithoutthepartnershipis:S=PN-11N-L-$3,995.Accordingtothecase,N,P,andLarerandomvariables,andso,Sisalsoarandomvariable.Nobeysanormaldistributionwithmean3,000andstandarddeviation1,000.PobeysadiscretedistributiongivenbyTable5.12,andLobeysauniformdistributionrangingfrom$5,040to$6,860.Tosolvethecase,werunaCrystalBallsimulationwith1000trials.TheassumptionvariablesareN,P,andL,andtheforecastvariableisS.Answertoassignmentquestions:(a)Afterrunninga1000-trialsimulationusingCrystalBall,wefoundthatSanjay'ssamplemeanmonthlysalaryis$10,722,whichisanestimateofSanjay'sexpectedmonthlysalaryatGentleLentil.IfSanjaydecidestoacceptthejobasaconsultant,hewouldmake$6,667permonth,whichislessthantheexpectedsalaryatGentleLentil.(b)FromthesameCrystalBallsimulation,wefoundthatthesamplestandarddeviationis$8,796,whichisanestimationofthetruestandarddeviationofSanjay'smonthlysalaryatGentleLentil.ThetruestandarddeviationisdifficulttocomputeinthisproblembecausewedonotifthevariablesN,P,andLareindependentofeachother.Evenifthevariablesareindependentofeachother,itisdifficulttocomputethestandarddeviationofSusingtheformulaintermsofN,P,andLgivenabove.(c)Thesearequantitativequestionsthatarenecessarytoconsiderbeforemakingadecisioninthiscasewithandwithoutthepartnershipoption:WhatisthedistributionofSanjay'ssalary?Whatisa95%confidenceintervalfortheexpectedmonthlysalary?WhatisP(S$5,000)?WhatisP(S$6,667)?Toanswerthosequestions,weuseCrystalBallagain.ThedistributionofSanjay'ssalary(withoutthepartnership)canbeestimatedusingthefollowingchart:Instructor’sManualChapter547ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.Withthepartnership,thedistributionlookslikethis:A95%confidenceintervalforthemonthlysalary(withoutthepartnership)is[$10,722-(1.96)($8,796/1000),$10,722+(1.96)($8,796/1000)]=[$10,177,$11,267].A95%confidenceintervalforthemonthlysalary(withthepartnership)is[$7,551-(1.96)($2,770/1000),$7,551+(1.96)($2,770/1000)]=[$7,379,$7,723].Probabilityofmakinglessthan$5,000permonthisapproximately0.288,andtheprobabilityofmakingmorethan$6,667permonthis0.649forbothalternatives(withandwithoutthepartnership).TOHEDGEORNOTTOHEDGE?FrequencyChart.000.007.014.021.02807142128($10,000)$1,250$12,500$23,750$35,0001,000Trials8OutliersForecast:Sanjaymonthlysalary(nopartnership)FrequencyChart.000.055.110.164.219054.75109.5164.2219$3,000$5,500$8,000$10,500$13,0001,000Trials0OutliersForecast:Sanjaymonthlysalary(partnership)Instructor’sManualChapter548ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.(a)Weusethesameh