BUS 660 Topic 1 Decision Analysis - Homework

Problem4-25: TheGormanManufacturingCompanymustdecidewhethertomanufactureacomponentpartatitsMilan, Michigan, plant or purchase the component part from a supplier. The resulting profit isdependentuponthedemandfortheproduct.Thefollowingpayofftableshowstheprojectedprofit(inthousandsofdollars): Thestate-of-natureprobabilitiesareP(s1)=0.35,P(s2)=0.35,andP(s3)=0.30. a. Useadecisiontreetorecommendadecision. b. UseEVPItodeterminewhetherGormanshouldattempttoobtainabetterestimateofdemand. c. A test market study of the potential demand for the product is expected to report either afavorable (F) or unfavorable (U) condition. The relevant conditional probabilities are asfollows: What is the probability that the market research report will be favorable? If required, round youranswertothreedecimalplaces. d. WhatisGorman'soptimaldecisionstrategy? e. Whatistheexpectedvalueofthemarketresearchinformation? Problem4-17: Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profitprojectionsappearpromising,butHemmingway'spresidentisconcernedbecausetheprobabilitythatthe R&D project will be successful is only 0.50. Furthermore, the president knows that even if theproject is successful, it will require that the company build a new production facility at a cost of $20million in order to manufacture the product. If the facility is built, uncertainty remains about thedemand and thus uncertainty about the profit that will be realized. Another option is that if the R&Dprojectissuccessful,thecompany couldsellthe rightsto the product foranestimated $25million.Underthisoption,thecompanywouldnotbuildthe$20millionproductionfacility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end ofthebranches. For example,therevenueprojection forthehighdemandoutcomeis$59million. However,thecostoftheR&Dproject($5million)andthecostoftheproductionfacility($20million)show the profit of this outcome to be $59 −$5 −$20 = $34 million. Branch probabilities are alsoshownforthechanceevents. a. AnalyzethedecisiontreetodeterminewhetherthecompanyshouldundertaketheR&Dproject. If itdoes,andiftheR&Dprojectissuccessful,whatshouldthecompanydo? Whatistheexpectedvalueofyourstrategy? b. Whatmustthesellingpricebeforthecompanytoconsidersellingtherightstotheproduct?Payoffforsellrightswouldhavetobe$25Mormore.Inordertorecoverthe$5MR&Dcost,thesellingpricewouldhavetobe$30Mormore. c. Develop a risk profile for the optimal strategy. If required, round your answers to two decimalplaces. Problem 4-23(Algorithmic) Supposethatyouaregivenadecisionsituationwiththreepossiblestatesofnature:S1,S2,andS3.The prior probabilities are P(S1) = 0.20, P(S2) = 0.50, and P(S3) = 0.30. With sample information I, P(I |S1) = 0.10, P(I | S2) = 0.05, and P(I | S3) = 0.20. Compute the revised or posterior probabilities: P(S1 |I),P(S2|I),andP(S3|I).Ifrequired,roundyouranswerstofourdecimalplaces. Problem 4-05(Algorithmic) In Americanfootball,touchdownsareworth6 points.Afterscoringatouchdown,thescoringteammaysubsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an assuredsuccess, while going for 2 points is successful only with probability p. Consider the following gamesituation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulationtime. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowingKilleen to score again. The Temple coach must decide whether to attempt a 1-point or 2-pointconversion after each touchdown.Ifthescoreis tiedat theend of regulationtime,thegamegoesintoovertime.The Temple coachbelievesthatthereisa42% chance thatTemple willwinifthe game goesinto overtime. The probability of successfully converting a 1-point conversion is 1.0. The probability ofsuccessfullyconvertinga2-pointconversionisp. 1. Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree forthedecisionof whether Temple'scoachshouldgofora1-pointconversionora2-pointconversionaftereachtouchdown.TheterminalnodesinthedecisiontreeshouldbeeitherWINorLOSEforTemple. b.AssumethataWINresultsinavalueof1.0andLOSEresultsinavalueof0.Further,assumethattheprobabilityofconvertinga2-pointconversionisp=35%.ShouldTemple'scoachgofora1-pointconversionor2-pointconversionafterscoringthefirsttouchdown? Problem 4-11(Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project.Amountsareinmillionsofdollars. SupposePDCisoptimisticaboutthepotentialfortheluxuryhigh-risecondominiumcomplexandthatthisoptimismleadsto aninitialsubjectiveprobabilityassessmentof0.81thatdemandwillbestrong(S1) and a corresponding probability of 0.19 that demand will be weak (S2). Assume the decisionalternativetobuildthelargecondominiumcomplexwasfoundtobeoptimalusingtheexpectedvalueapproach. Also, a sensitivity analysis was conducted for the payoffs associated with this decisionalternative.Itwasfoundthatthe large complexremainedoptimalaslongasthe payoffforthe strongdemandwasgreaterthanorequalto$18.05millionandaslongasthepayofffortheweakdemandwasgreaterthanorequalto-$13.05million. a. Consider the medium complex decision. How much could the payoff under strong demandincrease and still keep decision alternative d3 the optimal solution? If required, round youranswertotwodecimalplaces. b. Considerthesmallcomplexdecision.Howmuchcouldthepayoffunderstrongdemandincreaseand still keep decision alternatived3theoptimalsolution? Ifrequired,round youranswertotwodecimalplaces. Problem4-07 HudsonCorporationisconsideringthreeoptionsformanagingitsdataprocessingoperation:continuingwithitsown staff,hiringan outside vendortodothemanaging(referredtoasoutsourcing),orusinga combinationofitsown staffandanoutsidevendor.Thecostoftheoperationdependsonfuturedemand.Theannualcostofeachoption(inthousandsofdollars)dependsondemandasfollows: a. Ifthedemandprobabilitiesare0.2,0.5,and0.3,whichdecisionalternativewillminimizetheexpectedcostofthedataprocessingoperation? Whatistheexpectedannualcostassociatedwiththatrecommendation? b. Constructariskprofilefortheoptimaldecisioninpart(a). Theinputintheboxbelowwill notbegraded,butmaybereviewedandconsideredbyyourinstructor. Whatistheprobabilityofthecostexceeding$700,000?Ifrequired,roundyouranswertotwodecimalplaces. Problem4-15 The Lake Placid Town Council decided to build a new community center to be used for conventions,concerts,andotherpublicevents,butconsiderablecontroversysurroundstheappropriatesize.Manyinfluential citizens want a large center that would be a showcase for the area. But the mayor feels thatifdemanddoesnotsupportsuchacenter,thecommunitywilllosealargeamountofmoney.Toprovide structure for the decision process, the council narrowed the building alternatives to three sizes:small,medium, andlarge. Everybody agreedthatthe criticalfactor inchoosingthe bestsizeisthenumberofpeoplewhowillwanttousethenewfacility.Aregionalplanningconsultantprovideddemandestimatesunderthreescenarios:worst-case,base-case,andbest-case.Theworst-casescenariocorrespondstoasituationinwhichtourismdropssubstantially;thebase-casescenariocorrespondstoasituationinwhichLakePlacidcontinuestoattractvisitorsatcurrentlevels;andthebest-casescenariocorrespondstoasubstantialincreaseintourism.Theconsultanthasprovidedprobabilityassessmentsof0.10,0.60,and0.30fortheworst-case,base-case,andbest-casescenarios,respectively. Thetowncouncilsuggestedusingnetcashflowovera5-yearplanninghorizonasthecriterionfordeciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5-yearplanninghorizonhavebeendeveloped.Allcosts,includingtheconsultant'sfee,havebeenincluded. a. WhatdecisionshouldLakePlacidmakeusingtheexpectedvalueapproach? b. Identify the risk profiles for the medium and large alternatives.Riskprofileformedium-sizecommunitycenter:Graph(ii)Risk profileforlarge-sizecommunitycenter:Graph(iii) c. Computetheexpectedvalueofperfectinformation. Do you think it would be worth trying to obtain additional information concerning whichscenarioislikelytooccur? d. Suppose theprobabilityofthe worst-casescenarioincreasesto0.2,theprobabilityofthe base-casescenariodecreasesto0.5,andtheprobabilityofthebest-casescenarioremainsat0.3.What effect,if any,wouldthesechanges haveonthe decision recommendation? e. Theconsultanthassuggestedthatan expenditureof $150,000 on a promotional campaignover the planning horizon will effectively reduce the probability of the worst-case scenario tozero.Ifthecampaigncanbeexpectedtoalso increasetheprobabilityofthebest-casescenarioto0.4,isitagoodinvestment? Problem 4-21(Algorithmic) A real estate investor has the opportunity to purchase land currently zoned residential. If the countyboard approvesarequesttorezonethepropertyascommercialwithinthe next year,the investor willbeabletoleasethelandtoalargediscountfirmthatwantstoopenanewstoreontheproperty. However,ifthezoningchangeisnotapproved,theinvestorwill have to sellthe property ataloss.Profits(inthousandsofdollars)areshowninthefollowingpayofftable: a. If the probabilitythattherezoningwillbe approvedis0.5,whatdecisionisrecommended? Whatistheexpectedprofit? b. Theinvestorcanpurchasean optiontobuytheland.Undertheoption,theinvestormaintainstherightstopurchasethelandanytimeduringthenextthreemonthswhilelearningmoreaboutpossibleresistancetotherezoningproposalfromarearesidents.Probabilitiesareasfollows: Whatistheoptimaldecisionstrategyiftheinvestorusestheoptionperiodtolearnmoreabouttheresistancefromarearesidentsbeforemakingthepurchasedecision? c. Iftheoptionwillcosttheinvestoran additional$10,000,shouldtheinvestorpurchasetheoption? d. Whatisthemaximumthattheinvestorshouldbewillingtopayfortheoption?