constructoin project3.docx
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constructoin project3.docx
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constructoinproject3
CHAPTER19
INVENTORYMANAGEMENTWITHUNCERTAINDEMAND
LearningObjectives:
Aftercompletingthischapter,youshouldbeableto
1.Identifysomesituationswherethedemandforwithdrawingaproductfrominventoryisuncertain.
2.Describethetrade-offthatmustbeconsideredwhendevelopinganinventorypolicyforaproductwithuncertaindemand.
3.Explainwhyperishableproductswithuncertaindemandandstableproductswithuncertaindemandrequiredifferentkindsofinventorymodels.
4.Describeaninventorymodelforperishableproductswithuncertaindemand.
5.Applythismodeltofindtheoptimalorderquantity.
6.Describeacontinuous-reviewinventorymodelforstableproductswithuncertaindemand.
7.Applythismodeltochooseanorderquantity.
8.Applythismodeltodeterminetheinventorylevelatwhichanordershouldbeplacedwiththisorderquantity.
9.Describesomelargeinventorysystemsthatariseinpractice.
Wenowcontinuethefocusoftheprecedingchapteroninventorymanagement,butwithonekeydifference.Wehavebeenassumingthattheproductunderconsiderationininventoryhasaknowndemand,i.e.,thatwecanpredictwithreasonablecertaintywhenunitswillneedtobewithdrawnfrominventory.Wedropthisassumptioninthischapter,sowenowwillconsiderproductswithanuncertaindemand.
Thepredictabilityofdemanddependsgreatlyonthesituation.Wecertainlyhaveknowndemandwhentheproductisbeingwithdrawnfrominventoryatafixedratebecauseitactuallyisoneofseveralcomponentsbeingassembledintoalargerproductonanassemblyline.Similarly,amanufacturerhasaknowndemandforacustomproductininventorywhenitisproducingtheproduct(replenishinginventory)onlytosatisfyascheduleofordersalreadyreceivedfromaparticularcustomer.Awholesaleralsohasroughlyaknowndemandforaproductafteritsretailcustomershavedevelopedawellestablishedpatternforpurchasingtheproductmonthaftermonth.Thesearethetypesofsituationsconsideredintheprecedingchapter.
Bycontrast,aretailstoremanagerdoesnothavetheluxuryofknowingwhencustomerswillcomeintopurchaseagivenproduct.Iftheproductisanewone,predictinghowwellitwillcatchonmaybeparticularlydifficult.Similarly,awholesalersupplyinganumberofretailerswithanewproductmayhaveconsiderableuncertaintyaboutwhatthedemandwillbe.Salescanfluctuatewidelyfromonemonthtothenext.Consequently,amanufacturersellingtheproducttoanumberofwholesalers(perhapsincompetitionwithothermanufacturers)alsocanhavesignificantuncertaintyaboutthedemand.Weareconsideringthesekindsofsituationsinthischapter.
Evenwithuncertainty,itisnecessarytomakesomekindofforecastoftheexpecteddemandandwhatthevariabilitymightbe.Forexample,youmightusesomethinglikethePERTthree-estimateapproachdescribedinSection 8.4(makingamostlikelyestimate,anoptimisticestimate,andapessimisticestimate,andthenconvertingtheseestimatesintoaprobabilitydistribution).Insomeway,theforecastshouldbeexpressedinprobabilisticterms.Theprobabilitiesmightbequitesubjectiveinnature,aswiththetypicalpriorprobabilitiesofdecisionanalysisdiscussedinChapter 12,ortheymightbebasedonconsiderablehistoricalexperienceanddata.Atanyrate,themodelsinthischapterassumethatanestimatehasbeenmadeoftheprobabilitydistributionofwhatthedemandwillbeoveragivenperiod.
Averyimportantconsequenceofuncertaindemandisthegreatriskofincurringshortagesunlesstheinventoryismanagedcarefully.Anordertoreplenishtheinventoryneedstobeplacedwhilesomeinventorystillremains,becauseofthelaguntiltheordercanbefilled.Eventheamountofleadtimeneededtofilltheordermaybeuncertain.However,iftoomuchinventoryisreplenishedtoosoon,aheavypriceispaidbecauseofthehighcostofholdingalargeinventory.Aconstantthemethroughoutthechapteristheneedtofindthebesttrade-offbetweentheconsequencesofhavingtoomuchinventoryandofhavingtoolittle.
Wewillseparatelydiscussinventorymanagementfortwotypesofproducts.Onetypeisaperishableproduct,whichcanbecarriedininventoryforonlyaverylimitedperiodoftimebeforeitcannolongerbesold.Thesecondtypeisastableproduct,whichwillremainsellableindefinitely.Thesetwotypesneedtobehandledquitedifferently.
Thefirsttwosectionspresentacasestudyandthenageneralmodelforperishableproducts.Sections 19.3and19.4discussacasestudythatinvolvesastableproduct.TheinventorymodelthatunderliesthiscasestudyissummarizedinSection 19.5.Section19.6describesthelargeinventorysystemsthatcommonlyariseinpractice,includingmassivesystemsthathavebeeninstalledatIBMandHewlett-Packard.
19.1ACaseStudyforPerishableProducts—FreddietheNewsboy’sProblem
TheproblembeingaddressedinthiscasestudyactuallyisasimplifiedversionoftheoneforthecasestudyintroducedinSection16.1.Foreaseofexposition,wehavesimplifiedtheprobabilitydistributionofthedemandherebyhavingonlythreepossiblevaluesforthedemandinsteadofthe31consideredpreviously.ThetechniqueusedinChapter16toanalyzethisproblemwascomputersimulationwithCrystalBall.Inthissectionandthenext,wewilldevelopaninventorymodeltoaddressthesameprobleminarelativelystraightforwardway.Forcompleteness,werepeatthedescriptionoftheproblembelow.
Freddie’sProblem
Thisproblemconcernsanewsstandinaprominentdowntownlocationofamajorcity.Thenewsstandhasbeentherelongerthanmostpeoplecanremember.IthasalwaysbeenrunbyawellknowncharacternamedFreddie.(Nobodyseemstoknowhislastname.)HismanycustomersrefertohimaffectionatelyasFreddiethenewsboy,eventhoughheisconsiderablyolderthanmostofthem.
Freddiesellsawidevarietyofnewspapersandmagazines.ThemostexpensiveofthenewspapersisalargenationaldailycalledtheFinancialJournal.Ourcasestudyinvolvesthisnewspaper.
Theday’scopiesoftheFinancialJournalarebroughttothenewsstandearlyeachmorningbyadistributor.Anycopiesunsoldattheendofthedayarereturnedtothedistributorthenextmorning.(Thisisindeedaperishableproduct).However,toencourageorderingalargenumberofcopies,thedistributordoesgiveasmallrefundforunsoldcopies.
HereareFreddie’scostfigures.
Freddiepays$1.50percopydelivered.
Freddiesellsitat$2.50percopy.
Freddie’srefundis$0.50perunsoldcopy.
Partiallybecauseoftherefund,Freddiealwayshastakenaplentifulsupply.However,hehasbecomeconcernedaboutpayingsomuchforcopiesthatthenhavetoreturnunsold,particularlysincethishasbeenoccurringnearlyeveryday.Henowthinkshemightbebetteroffbyorderingonlyaminimalnumberofcopiesandsavingthisextracost.
Toinvestigatethisfurther,Freddiehasbeenkeepingarecordofhisdailysales.IncontrasttothenumberspresentedinChapter16,weassumenowthatthisiswhathehasfound.
Freddiesells9copieson30%ofthedays.
Freddiesells10copieson40%ofthedays.
Freddiesells11copieson30%ofthedays.
SohowmanycopiesshouldFreddieorderfromthedistributorperday?
(Thinkaboutitbeforereadingon.)
ApplyingBayes’DecisionRuletoFreddie’sProblem
OneapproachtothisproblemistoapplydecisionanalysisasdescribedinChapter 12.Specifically,Bayes’decisionruleintroducedinSection 12.2isusedasoutlinedbelow.
TheprocedureinvolvesfillingoutthepayofftableshowninFigure19.1.Column Bliststhedecisionalternativesthatdeserveconsideration,namely,toorder9,10,or11copiesperdayfromthedistributor.Foreachofthesealternatives,Freddie’sprofitonagivendayisdeterminedbyhowmanyrequeststopurchaseacopyoftheFinancialJournaloccurthatday,sothesepossiblenumbersofpurchaserequests(thepossiblestatesofnature)arelistedincellsD4:
F9.TherelativelikelihoodofthesenumbersofpurchaserequestsareenteredinPriorProbability(D9:
F9)asthepriorprobabilitiesofthesestatesofnature.
Figure19.1ThisExceltemplateinyourMSCoursewareshowsthatFreddiethenewsboymaximizeshisexpectedprofitbyordering10copieseachday.
ThepayofffromFreddie’sdecision,giventhestateofnature,istheprofitforthatday.Thisprofitis
Profit=salesincome-purchasecost+refund.
Forexample,ifFreddieorders11copiesfromthedistributorandthestateofnatureturnsouttobe9forthatday(9copiesaresold),hisprofitis
Profit=9($2.50)-11($1.50)+2($0.50)=$7.00.
CalculatingtheprofitinthiswayforeachofthecombinationsofadecisionalternativeandapossiblestateofnatureyieldsthepayofftableshownincellsB3:
F9ofFigure19.1.ApplyingBayes’decisionrulewiththisExceltemplateinvolvescalculatingtheexpectedpayoff(EP)foreachalternativebyusingtheindicatedequationsenteredintoExpectedPayoff(H5:
H7).(Ifyouhaven’tstudiedthistopicinChapter12,notethateachoftheseequationsissimplycalculatingthestatisticalaverageofthepayoffs.)Therulethenselectsthealternativewiththelargestexpectedpayoff($9.40).
Conclusion:
Freddie’smostprofitablealternativeinthelongrunistoorder10copies,sincethiswillprovideanaveragedailyprofitof$9.40,versus$9.00foreitheroftheotheralternatives.
Inthenextsection,youwillseeashortcutfordrawingthissameconclusion.
REVIEWQUESTIONS
1.Whatisthetrade-offthatFreddiethenewsboyshouldconsiderinmakinghisdecision?
2.WhyareFreddie’sdecisionalternativesli
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