Chapter6

NetworkDesigninan

UncertainEnvironmentSupplyChainManagement

(3rdEdition)

6-1OutlineTheImpactofUncertaintyonNetworkDesignDecisionsDiscountedCashFlowAnalysisRepresentationsofUncertaintyEvaluatingNetworkDesignDecisionsUsingDecisionTreesAMTires:EvaluationofSupplyChainDesignDecisionsUnderUncertaintyMakingSupplyChainDecisionsUnderUncertaintyinPracticeSummaryofLearningObjectives2TheImpactofUncertainty

onNetworkDesignSupplychaindesigndecisionsincludeinvestmentsinnumberandsizeofplants,numberoftrucks,numberofwarehousesThesedecisionscannotbeeasilychangedintheshort-termTherewillbeagooddealofuncertaintyindemand,prices,exchangerates,andthecompetitivemarketoverthelifetimeofasupplychainnetworkTherefore,buildingflexibilityintosupplychainoperationsallowsthesupplychaintodealwithuncertaintyinamannerthatwillmaximizeprofits3DiscountedCashFlowAnalysisSupplychaindecisionsareinplaceforalongtime,sotheyshouldbeevaluatedasasequenceofcashflowsoverthatperiodDiscountedcashflow(DCF)analysisevaluatesthepresentvalueofanystreamoffuturecashflowsandallowsmanagerstocomparedifferentcashflowstreamsintermsoftheirfinancialvalueBasedonthetimevalueofmoney–adollartodayisworthmorethanadollartomorrow4DiscountedCashFlowAnalysisCompareNPVofdifferentsupplychaindesignoptionsTheoptionwiththehighestNPVwillprovidethegreatestfinancialreturn5NPVExample:TripsLogisticsHowmuchspacetoleaseinthenextthreeyearsDemand=100,000unitsRequires1,000sq.ft.ofspaceforevery1,000unitsofdemandRevenue=$1.22perunitofdemandDecisioniswhethertosignathree-yearleaseorobtainwarehousingspaceonthespotmarketThree-yearlease:cost=$1persq.ft.Spotmarket:cost=$1.20persq.ft.k=0.16NPVExample:TripsLogisticsForleasingwarehousespaceonthespotmarket:Expectedannualprofit=100,000x$1.22–100,000x$1.20=$2,000Cashflow=$2,000ineachofthenextthreeyears7NPVExample:TripsLogisticsForleasingwarehousespacewithathree-yearlease:Expectedannualprofit=100,000x$1.22–100,000x$1.00=$22,000Cashflow=$22,000ineachofthenextthreeyearsTheNPVofsigningtheleaseis$54,711higher;therefore,themanagerdecidestosigntheleaseHowever,uncertaintyindemandandcostsmaycausethemanagertorethinkhisdecision8RepresentationsofUncertaintyBinomialRepresentationofUncertaintyOtherRepresentationsofUncertainty9BinomialRepresentations

ofUncertaintyWhenmovingfromoneperiodtothenext,thevalueoftheunderlyingfactor(e.g.,demandorprice)hasonlytwopossibleoutcomes–upordownTheunderlyingfactormovesupbyafactororu>1withprobabilityp,ordownbyafactord<1withprobability1-pAssumingapricePinperiod0,forthemultiplicativebinomial,thepossibleoutcomesforthenextfourperiods:Period1:Pu,PdPeriod2:Pu2,Pud,Pd2Period3:Pu3,Pu2d,Pud2,Pd3

Period4:Pu4,Pu3d,Pu2d2,Pud3,Pd4

10BinomialRepresentations

ofUncertaintyIngeneral,formultiplicativebinomial,periodThasallpossibleoutcomesPutd(T-t),fort=0,1,…,TFromstatePuad(T-a)inperiodt,thepricemaymoveinperiodt+1toeitherPua+1d(T-a)withprobabilityp,orPuad(T-a)+1withprobability(1-p)RepresentedasthebinomialtreeshowninFigure6.1(p.140)11BinomialRepresentations

ofUncertaintyFortheadditivebinomial,thestatesinthefollowingperiodsare:Period1:P+u,P-dPeriod2:P+2u,P+u-d,P-2dPeriod3:P+3u,P+2u-d,P+u-2d,P-3dPeriod4:P+4u,P+3u-d,P+2u-2d,P+u-3d,P-4dIngeneral,fortheadditivebinomial,periodThasallpossibleoutcomesP+tu-(T-t)d,fort=0,1,…,T12EvaluatingNetworkDesignDecisionsUsingDecisionTreesAmanagermustmakemanydifferentdecisionswhendesigningasupplychainnetworkManyoftheminvolveachoicebetweenalong-term(orlessflexible)optionandashort-term(ormoreflexible)optionIfuncertaintyisignored,thelong-termoptionwillalmostalwaysbeselectedbecauseitistypicallycheaperSuchadecisioncaneventuallyhurtthefirm,however,becauseactualfuturepricesordemandmaybedifferentfromwhatwasforecastedatthetimeofthedecisionAdecisiontreeisagraphicdevicethatcanbeusedtoevaluatedecisionsunderuncertainty13DecisionTreeMethodologyIdentifythedurationofeachperiod(month,quarter,etc.)andthenumberofperiodsToverthewhichthedecisionistobeevaluated.Identifyfactorssuchasdemand,price,andexchangerate,whosefluctuationwillbeconsideredoverthenextTperiods.Identifyrepresentationsofuncertaintyforeachfactor;thatis,determinewhatdistributiontousetomodeltheuncertainty.Identifytheperiodicdiscountratekforeachperiod.Representthedecisiontreewithdefinedstatesineachperiod,aswellasthetransitionprobabilitiesbetweenstatesinsuccessiveperiods.StartingatperiodT,workbacktoperiod0,identifyingtheoptimaldecisionandtheexpectedcashflowsateachstep.Expectedcashflowsateachstateinagivenperiodshouldbediscountedbackwhenincludedinthepreviousperiod.14DecisionTreeMethodology:

TripsLogisticsDecidewhethertoleasewarehousespaceforthecomingthreeyearsandthequantitytoleaseLong-termleaseiscurrentlycheaperthanthespotmarketrateThemanageranticipatesuncertaintyindemandandspotpricesoverthenextthreeyearsLong-termleaseischeaperbutcouldgounusedifdemandislowerthanforecast;futurespotmarketratescouldalsodecreaseSpotmarketratesarecurrentlyhigh,andthespotmarketwouldcostalotiffuturedemandishigherthanexpected15TripsLogistics:ThreeOptionsGetallwarehousingspacefromthespotmarketasneededSignathree-yearleaseforafixedamountofwarehousespaceandgetadditionalrequirementsfromthespotmarketSignaflexibleleasewithaminimumchangethatallowsvariableusageofwarehousespaceuptoalimitwithadditionalrequirementfromthespotmarket16TripsLogistics1000sq.ft.ofwarehousespaceneededfor1000unitsofdemandCurrentdemand=100,000unitsperyearBinomialuncertainty:Demandcangoupby20%with

p=0.5ordownby20%with1-p=0.5Leaseprice=$1.00persq.ft.peryearSpotmarketprice=$1.20persq.ft.peryearSpotpricescangoupby10%withp=0.5ordownby10%with1-p=0.5Revenue=$1.22perunitofdemandk=0.117TripsLogisticsDecisionTree

(Fig.6.2)D=144p=$1.45D=144p=$1.19D=96p=$1.45D=144p=$0.97D=96p=$1.19D=96p=$0.97D=64p=$1.45D=64p=$1.19D=64p=$0.97D=120p=$1.32D=120p=$1.08D=80p=$1.32D=80p=$1.32D=100p=$1.200.250.250.250.250.250.250.250.25Period0Period1Period218TripsLogisticsExampleAnalyzetheoptionofnotsigningaleaseandobtainingallwarehousespacefromthespotmarketStartwithPeriod2andcalculatetheprofitateachnodeForD=144,p=$1.45,inPeriod2: C(D=144,p=1.45,2)=144,000x1.45=$208,800 P(D=144,p=1.45,2)=144,000x1.22–C(D=144,p=1.45,2)=175,680-208,800=-$33,120ProfitatothernodesisshowninTable6.119TripsLogisticsExampleExpectedprofitateachnodeinPeriod1istheprofitduringPeriod1plusthepresentvalueoftheexpectedprofitinPeriod2ExpectedprofitEP(D=,p=,1)atanodeistheexpectedprofitoverallfournodesinPeriod2thatmayresultfromthisnodePVEP(D=,p=,1)isthepresentvalueofthisexpectedprofitandP(D=,p=,1),andthetotalexpectedprofit,isthesumoftheprofitinPeriod1andthepresentvalueoftheexpectedprofitinPeriod220TripsLogisticsExampleFromnodeD=120,p=$1.32inPeriod1,therearefourpossiblestatesinPeriod2EvaluatetheexpectedprofitinPeriod2overallfourstatespossiblefromnodeD=120,p=$1.32inPeriod1tobe EP(D=120,p=1.32,1)= 0.25xP(D=144,p=1.45,2)+ 0.25xP(D=144,p=1.19,2)+ 0.25xP(D=96,p=1.45,2)+ 0.25xP(D=96,p=1.19,2) =0.25x(-33,120)+0.25x4,320+0.25x(-22,080)+0.25x2,880 =-$12,00021TripsLogisticsExampleThepresentvalueofthisexpectedvalueinPeriod1is PVEP(D=12,p=1.32,1) =EP(D=120,p=1.32,1)/(1+k) =-$12,000/(1+0.1) =-$10,909ThetotalexpectedprofitP(D=120,p=1.32,1)atnodeD=120,p=1.32inPeriod1isthesumoftheprofitinPeriod1atthisnode,plusthepresentvalueoffutureexpectedprofitspossiblefromthisnode P(D=120,p=1.32,1)=[(120,000x1.22)-(120,000x1.32)]+ PVEP(D=120,p=1.32,1) =-$12,000+(-$10,909)=-$22,909ThetotalexpectedprofitfortheothernodesinPeriod1isshowninTable6.222TripsLogisticsExampleForPeriod0,thetotalprofitP(D=100,p=120,0)isthesumoftheprofitinPeriod0andthepresentvalueoftheexpectedprofitoverthefournodesinPeriod1 EP(D=100,p=1.20,0) =0.25xP(D=120,p=1.32,1)+ =0.25xP(D=120,p=1.08,1)+ =0.25xP(D=96,p=1.32,1)+ =0.25xP(D=96,p=1.08,1) =0.25x(-22,909)+0.25x32,073+0.25x(-15,273)+0.25x21,382 =$3,818 PVEP(D=100,p=1.20,0)=EP(D=100,p=1.20,0)/(1+k) =$3,818/(1+0.1)=$3,47123TripsLogisticsExample P(D=100,p=1.20,0) =100,000x1.22-100,000x1.20+ PVEP(D=100,p=1.20,0) =$2,000+$3,471=$5,471Therefore,theexpectedNPVofnotsigningtheleaseandobtainingallwarehousespacefromthespotmarketisgivenbyNPV(SpotMarket)=$5,47124TripsLogisticsExampleUsingthesameapproachfortheleaseoption,NPV(Lease)=$38,364Recallthatwhenuncertaintywasignored,theNPVfortheleaseoptionwas$60,182However,themanagerwouldprobablystillprefertosignthethree-yearleasefor100,000sq.ft.becausethisoptionhasthehigherexpectedprofit25EvaluatingFlexibility

UsingDecisionTreesDecisiontreemethodologycanbeusedtoevaluateflexibilitywithinthesupplychainSupposethemanageratTripsLogisticshasbeenofferedacontractwhere,foranupfrontpaymentof$10,000,thecompanywillhavetheflexibilityofusingbetween60,000sq.ft.and100,000sq.ft.ofwarehousespaceat$1persq.ft.peryear.Tripsmustpay$60,000forthefirst60,000sq.ft.andcanthenuseupto40,000sq.ft.ondemandat$1persq.ft.asneeded.Usingthesameapproachasbefore,theexpectedprofitofthisoptionis$56,725ThevalueofflexibilityisthedifferencebetweentheexpectedpresentvalueoftheflexibleoptionandtheexpectedpresentvalueoftheinflexibleoptionsThethreeoptionsarelistedinTable6.7,wheretheflexibleoptionhasanexpectedpresentvalue$8,361greaterthantheinflexibleleaseoption(includingtheupfront$10,000payment)26AMTires:EvaluationofSupplyChainDesignDecisionsUnderUncertaintyDedicatedCapacityof100,000intheUnitedStatesand50,000inMexicoPeriod2EvaluationPeriod1EvaluationPeriod0EvaluationFlexibleCapacityof100,000intheUnitedStatesand50,000inMexicoPeriod2EvaluationPeriod1EvaluationPeriod0Evaluation27EvaluatingFacilityInvestments:AMTiresU.S.ExpectedDemand=100,000;MexicoExpectedDemand=50,0001US$=9