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Instructor’sManualChapter10115ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.Chapter10IChapterOutline10.1ManagementScienceModelsintheAirlineIndustryDiscussionofthefollowingapplicationsofmanagementscienceintheairlineindustry:1.Hub-and-spokeconfiguration2.Demandforecast3.Flightschedule4.Fleetassignment5.Crewpairing6.Overbooking7.RevenuemanagementFurtherdiscussiononrevenuemanagementShadowprices,simulationmodeling,andbid-pricecontrolpolicies10.2ManagementScienceModelsintheFinancialInvestmentManagementIndustryManagementscienceapplicationsin:1.Analysisoffinancialdata2.Forecastingfutureperformanceofassets3.Constructionandmanagementofefficientportfolios4.Determiningtradingstrategiesthatminimizetradingcost5.Evaluationoffinancialassetssuchasoptionsandotherderivativesecurities10.3AYearintheLifeofaManufacturingCompanyAnalysisofseveralmodelingproblemsfortheLexingtonLaserCorporationIIAnswerstoChapterCasesSLOANINVESTORS,PARTII(a)Weusethenon-linearoptimizationmodelfortheportfoliooptimizationproblemdiscussedinChapter8.Belowweshowtheefficientfrontiersforeachofthesixmonthsintheperiodunderconsideration.Instructor’sManualChapter10116ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.(b)Thenexttablesummarizesthecomputations.Dow30IndexMonthExpectedReturnStandardDeviationJanuary0.4823%2.7920%February0.8558%2.7664%March0.9501%2.7144%April-0.2179%2.6855%May0.2604%2.7477%June0.4071%2.7323%Cumulative2.7379%6.7115%(c)Thenexttablesummarizesthecomputations.January960%1%2%3%4%5%6%0.0000%1.0000%2.0000%3.0000%4.0000%5.0000%MinimumRiskTargetReturnFebruary960%5%10%15%0.0000%1.0000%2.0000%3.0000%4.0000%5.0000%6.0000%MinimumRiskTargetReturnMarch960%2%4%6%8%10%12%0.0000%2.0000%4.0000%6.0000%8.0000%10.0000%12.0000%14.0000%MinimumRiskTargetReturnApril960%5%10%15%20%0.0000%5.0000%10.0000%15.0000%20.0000%MinimumRiskTargetReturnMay960%2%4%6%8%10%12%14%0.0000%5.0000%10.0000%15.0000%MinimumRiskTargetReturnJune960%2%4%6%8%10%12%0.0000%2.0000%4.0000%6.0000%8.0000%10.0000%12.0000%14.0000%MinimumRiskTargetReturnInstructor’sManualChapter10117ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.OptimizedPortfolioMonthExpectedReturnStandardDeviationJanuary4.1329%2.7920%February9.2251%2.7664%March5.6300%2.7144%April4.0553%2.6855%May4.1294%2.7477%June4.1752%2.7323%Cumulative31.3478%6.7115%(d)Studentanswerswillvary.REVENUEMANAGEMENTATATLANTICAIR(a)Inthisproblem,PQ=250andPY=750.Hence,wewanttofindL*suchthatP(NY=L*)=(750–250)/750=0.667.Usingthestandardnormaldistributiontables,wefindthatP(Z=0.43)0.667.Therefore,wehaveL*=0.43x5.57+27.86=30.26istheoptimalprotectionlevel.Thecorrespondingoptimalexpectedrevenueis$24,911perflightleg.(b)Usingthecomputermodelforaplanewithacapacityof75seats,weobtainthattheoptimalexpectedrevenueperflightlegis$31,161.Sincewehave4x365=1,460flightlegsperyear,thisrepresentsanexpectedrevenueof$45,495,060peryear,thatis,anincrementof$45,495,060-$24,911x1,460=$9,125,000peryearovertherevenuesfromthecurrent50-seatplane.Theadditionaloperationcostsare$2,000x365x4=$2,920,000peryear.Hence,thenetcashflowifAtlanticAiracceptstheofferwillbe$9,125,000-$2,920,000-$1,500,000=$4,705,000.Therefore,AtlanticAirshouldaccepttheoffer.(c)ByacceptingCCG’sgroup,thecapacityoftheplanewillbereducedto34seats.Thisrepresentsadropto$20,911inoptimalexpectedrevenues,thatis,wehaveareductionof$4,000inrevenues.Therefore,AtlanticAirshouldchargetoCCGatleast$4,000/16=$250foraone-wayticket.ASTRATEGICALLIANCEFORTHELEXINGTONLASERCORPORATION(a)Thedecisiontreeisshownonthenextpage.WedenotebyBthebestcasescenarioforAspenandbyWtheworstcasescenarioforAspen.WedenotebyBforecastthescenarioinwhichthemarketstudyiscommissionedandthereportisthatthebestcasescenarioforAspenwilloccur.Similarly,WforecastrepresentsthescenarioinwhichtheworstcasescenarioforAspenisforecast.Accordingtotheinformationgiven,noticethatP(Bforecast|W)=P(Wforecast|B)=0.30.Usingthelawsofconditionalprobabilities,aswellasBayes'law,weobtainthatP(Bforecast)=P(Bforecast|B)xP(B)+P(BInstructor’sManualChapter10118ManualtoaccompanyData,Models&Decisions:TheFundamentalsofManagementSciencebyBertsimasandFreund.Copyright2000,South-WesternCollegePublishing.PreparedbyManuelNunez,ChapmanUniversity.forecast|W)xP(W)=(0.7)(0.7)+(0.3)(0.3)=0.58.Similarly,P(Wforecast)=0.42.Also,P(B|Bforecast)=P(Bforecast|B)xP(B)/P(Bforecast)=(0.7)(0.7)/(0.58)=0.845.Furthermore,P(W|Bforecast)=0.155,P(B|Wforecast)=0.5,andP(W|Bforecast)=0.5.WeassumethatifLLCwaitsforsixmonths,thenitwillmake$5,500,000x0.20=$1,100,000aftertaxifthebestcasescenariooccurs.(b)Thedecisiontreedoesnotcaptureintermediatescenarios,thatis,theprobabilitydistributionofthescenarios.Assumingthatthereonlyaretwoscenarios(bestan