11ManagingEconomiesofScaleinaSupplyChain:CycleInventoryLearningObjectivesBalancetheappropriatecoststochoosetheoptimallotsizeandcycleinventoryinasupplychain.Understandtheimpactofquantitydiscountsonlotsizeandcycleinventory.Deviseappropriatediscountingschemesforasupplychain.Understandtheimpactoftradepromotionsonlotsizeandcycleinventory.Identifymanagerialleversthatreducelotsizeandcycleinventoryinasupplychainwithoutincreasingcost.RoleofCycleInventory

inaSupplyChainLotorbatchsizeisthequantitythatastageofasupplychaineitherproducesorpurchasesatatimeCycleinventoryistheaverageinventoryinasupplychainduetoeitherproductionorpurchasesinlotsizesthatarelargerthanthosedemandedbythecustomer Q:Quantityinalotorbatchsize

D:DemandperunittimeInventoryProfileFigure11-1RoleofCycleInventory

inaSupplyChainAverageflowtimeresultingfromcycleinventoryRoleofCycleInventory

inaSupplyChainLowercycleinventoryhasShorteraverageflowtimeLowerworkingcapitalrequirementsLowerinventoryholdingcostsCycleinventoryisheldtoTakeadvantageofeconomiesofscaleReducecostsinthesupplychainRoleofCycleInventory

inaSupplyChainAveragepricepaidperunitpurchasedisakeycostinthelot-sizingdecision Materialcost=CFixedorderingcostincludesallcoststhatdonotvarywiththesizeoftheorderbutareincurredeachtimeanorderisplaced Fixedorderingcost=SHoldingcostisthecostofcarryingoneunitininventoryforaspecifiedperiodoftime Holdingcost=H=hCRoleofCycleInventory

inaSupplyChainPrimaryroleofcycleinventoryistoallowdifferentstagestopurchaseproductinlotsizesthatminimizethesumofmaterial,ordering,andholdingcostsIdeally,cycleinventorydecisionsshouldconsidercostsacrosstheentiresupplychainInpractice,eachstagegenerallymakesitsownsupplychaindecisionsIncreasestotalcycleinventoryandtotalcostsinthesupplychainRoleofCycleInventory

inaSupplyChainEconomiesofscaleexploitedinthreetypicalsituationsAfixedcostisincurredeachtimeanorderisplacedorproducedThesupplierofferspricediscountsbasedonthequantitypurchasedperlotThesupplieroffersshort-termpricediscountsorholdstradepromotionsEstimatingCycleInventoryRelatedCostsinPracticeInventoryHoldingCostCostofcapitalwhere

E =amountofequity

D =amountofdebt

Rf =risk-freerateofreturn

b =thefirm’sbeta

MRP =marketriskpremium

Rb =rateatwhichthefirmcanborrowmoney

t =taxrateInventoryHoldingCostCostofcapitalEstimatingCycleInventoryRelatedCostsinPracticeAdjustedforpre-taxsettingEstimatingCycleInventoryRelatedCostsinPracticeInventoryHoldingCostObsolescencecostHandlingcostOccupancycostMiscellaneouscostsTheft,security,damage,tax,insuranceEstimatingCycleInventoryRelatedCostsinPracticeOrderingCostBuyertimeTransportationcostsReceivingcostsOthercostsEconomiesofScale

toExploitFixedCostsLotsizingforasingleproduct(EOQ) D

= Annualdemandoftheproduct S

=

Fixedcostincurredperorder C

=

Costperunit H

=

HoldingcostperyearasafractionofproductcostBasicassumptionsDemandissteadyatD

unitsperunittimeNoshortagesareallowedReplenishmentleadtimeisfixedEconomiesofScale

toExploitFixedCostsMinimizeAnnualmaterialcostAnnualorderingcostAnnualholdingcostLotSizingforaSingleProductLotSizingforaSingleProductFigure11-2LotSizingforaSingleProductTheeconomicorderquantity(EOQ)TheoptimalorderingfrequencyEOQExampleAnnualdemand,D=1,000x12=12,000unitsOrdercostperlot,S=$4,000Unitcostpercomputer,C=$500Holdingcostperyearasafractionofunitcost,h=0.2EOQExampleEOQExampleLotsizereducedtoQ=200unitsLotSizeandOrderingCostIfthelotsizeQ*=200,howmuchshouldtheorderingcostbereduced?Desiredlotsize,Q*=200Annualdemand,D=1,000×12=12,000unitsUnitcostpercomputer,C=$500Holdingcostperyearasafractionofinventoryvalue,h=0.2ProductionLotSizingTheentirelotdoesnotarriveatthesametimeProductionoccursataspecifiedratePInventorybuildsupatarateofP

–DAnnualsetupcostAnnualholdingcostAggregatingMultipleProducts

inaSingleOrderSavingsintransportationcostsReducesfixedcostforeachproductLotsizeforeachproductcanbereducedCycleinventoryisreducedSingledeliveryfrommultiplesuppliersorsingletruckdeliveringtomultipleretailersReceivingandloadingcostsreducedLotSizingwithMultiple

ProductsorCustomersOrdering,transportation,andreceivingcostsgrowwiththevarietyofproductsorpickuppointsLotsizesandorderingpolicythatminimizetotalcost

Di: Annualdemandforproducti

S: Ordercostincurredeachtimeanorderisplaced,independentofthevarietyofproductsintheorder

si: Additionalordercostincurredifproducti

isincludedintheorderLotSizingwithMultiple

ProductsorCustomersThreeapproachesEachproductmanagerordershisorhermodelindependentlyTheproductmanagersjointlyordereveryproductineachlotProductmanagersorderjointlybutnoteveryordercontainseveryproduct;thatis,eachlotcontainsaselectedsubsetoftheproductsMultipleProductsOrderedandDeliveredIndependentlyDemand

DL

=12,000/yr,DM

=1,200/yr,DH

=120/yrCommonordercost

S

=$4,000Product-specificordercost

sL

=$1,000,sM

=$1,000,sH=$1,000Holdingcost

h

=0.2Unitcost

CL

=$500,CM=$500,CH=$500MultipleProductsOrderedandDeliveredIndependentlyLiteproMedproHeavyproDemandperyear12,0001,200120Fixedcost/order$5,000$5,000$5,000Optimalordersize1,095346110Cycleinventory54817355Annualholdingcost$54,772$17,321$5,477Orderfrequency11.0/year3.5/year1.1/yearAnnualorderingcost$54,772$17,321$5,477Averageflowtime2.4weeks7.5weeks23.7weeksAnnualcost$109,544$34,642$10,954Table11-1Totalannualcost=$155,140LotsOrderedandDeliveredJointlyProductsOrderedandDeliveredJointlyAnnualordercost=9.75x7,000=$68,250Annualorderingandholdingcost =$61,512+$6,151+$615+$68,250 =$136,528ProductsOrderedandDeliveredJointlyLiteproMedproHeavyproDemandperyear(D)12,0001,200120Orderfrequency(n?)9.75/year9.75/year9.75/yearOptimalordersize(D/n?)1,23012312.3Cycleinventory61561.56.15Annualholdingcost$61,512$6,151$615Averageflowtime2.67weeks2.67weeks2.67weeksTable11-2AggregationwithCapacityConstraintW.W.Graingerexample

Demandperproduct,Di

=10,000 Holdingcost,h

=

0.2 Unitcostperproduct,Ci

=

$50 Commonordercost,S

=

$500 Supplier-specificordercost,si

=

$100AggregationwithCapacityConstraintAnnualholdingcostpersupplierAggregationwithCapacityConstraintTotalrequiredcapacitypertruck=4x671=2,684unitsTruckcapacity=2,500unitsOrderquantityfromeachsupplier=2,500/4=625Orderfrequencyincreasedto10,000/625=16Annualordercostpersupplierincreasesto$3,600Annualholdingcostpersupplierdecreasesto$3,125.LotsOrderedandDeliveredJointlyforaSelectedSubsetStep1: IdentifythemostfrequentlyorderedproductassumingeachproductisorderedindependentlyStep2: Forallproductsi≠

i*,evaluatetheorderingfrequencyLotsOrderedandDeliveredJointlyforaSelectedSubsetStep3: Foralli≠

i*,evaluatethefrequencyofproducti

relativetothemostfrequentlyorderedproducti*tobemiStep4: Recalculatetheorderingfrequencyofthemostfrequentlyorderedproducti*tobenLotsOrderedandDeliveredJointlyforaSelectedSubsetStep5: Evaluateanorderfrequencyofni=n/mi

andthetotalcostofsuchanorderingpolicyTailoredaggregation–higher-demandproductsorderedmorefrequentlyandlower-demandproductsorderedlessfrequentlyOrderedandDeliveredJointly–FrequencyVariesbyOrderApplyingStep1ThusOrderedandDeliveredJointly–FrequencyVariesbyOrderApplyingStep2ApplyingStep3OrderedandDeliveredJointly–FrequencyVariesbyOrderLiteproMedproHeavyproDemandperyear(D)12,0001,200120Orderfrequency(n?)11.47/year5.74/year2.29/yearOptimalordersize(D/n?)1,04620952Cycleinventory523104.526Annualholdingcost$52,307$10,461$2,615Averageflowtime2.27weeks4.53weeks11.35weeksTable11-3OrderedandDeliveredJointly–FrequencyVariesbyOrderApplyingStep4ApplyingStep5Annualordercost Totalannualcost$130,767EconomiesofScaleto

ExploitQuantityDiscountsLotsize-baseddiscount–discountsbasedonquantityorderedinasinglelotVolumebaseddiscount–

discountisbasedontotalquantitypurchasedoveragivenperiodTwocommonschemesAll-unitquantitydiscountsMarginalunitquantitydiscountormulti-blocktariffsQuantityDiscountsTwobasicquestionsWhatistheoptimalpurchasingdecisionforabuyerseekingtomaximizeprofits?Howdoesthisdecisionaffectthesupplychainintermsoflotsizes,cycleinventories,andflowtimes?Underwhatconditionsshouldasupplierofferquantitydiscounts?Whatareappropriatepricingschedulesthatasupplierseekingtomaximizeprofitsshouldoffer?All-UnitQuantityDiscountsPricingschedulehasspecifiedquantitybreakpointsq0,q1,…,qr,whereq0=0Ifanorderisplacedthatisatleastaslargeasqibutsmallerthanqi+1,theneachunithasanaverageunitcostofCiUnitcostgenerallydecreasesasthequantityincreases,i.e.,C0>C1>…>Cr

Objectiveistodecideonalotsizethatwillminimizethesumofmaterial,order,andholdingcostsAll-UnitQuantityDiscountsFigure11-3All-UnitQuantityDiscountsStep1: EvaluatetheoptimallotsizeforeachpriceCi,0≤i≤rasfollowsAll-UnitQuantityDiscountsStep2: WenextselecttheorderquantityQ*iforeachpriceCi1.2.3.Case3canbeignoredasitisconsideredforQi+1ForCase1if,thensetQ*i=QiIf,thenadiscountisnotpossibleSetQ*i =qitoqualifyforthediscountedpriceofCiAll-UnitQuantityDiscountsStep3: CalculatethetotalannualcostoforderingQ*iunitsAll-UnitQuantityDiscountsStep4: SelectQ*iwiththelowesttotalcostTCiCutoffpriceAll-UnitQuantityDiscountExampleOrderQuantityUnitPrice0–4,999$3.005,000–9,999$2.9610,000ormore$2.92q0=0,q1=5,000,q2=10,000C0=$3.00,C1=$2.96,C2=$2.92D=120,000/year,S=$100/lot,h=0.2All-UnitQuantityDiscountExampleStep1Step2Ignorei=0becauseQ0=6,324>q1=5,000Fori=1,2All-UnitQuantityDiscountExampleStep3Lowesttotalcostisfori=2Order

bottlesperlotat$2.92perbottleMarginalUnitQuantityDiscountsMulti-blocktariffs–themarginalcostofaunitthatdecreasesatabreakpointForeachvalueofi,0

≤i≤r,letVi

bethecostoforderingqi

unitsMarginalUnitQuantityDiscountsFigure11-4MarginalUnitQuantityDiscountsMaterialcostofeachorderQ

isVi+(Q–qi)CiTotalannualcostMarginalUnitQuantityDiscountsStep1: EvaluatetheoptimallotsizeforeachpriceCiMarginalUnitQuantityDiscountsStep2: SelecttheorderquantityQi*foreachpriceCi1.2.3.MarginalUnitQuantityDiscountsStep3: CalculatethetotalannualcostoforderingQi*Step4: SelecttheordersizeQi*withthelowesttotalcostTCiMarginalUnitQuantityDiscountExampleOriginaldatanowamarginaldiscountOrderQuantityUnitPrice0–4,999$3.005,000–9,999$2.9610,000ormore$2.92q0=0,q1=5,000,q2=10,000C0=$3.00,C1=$2.96,C2=$2.92D=120,000/year,S=$100/lot,h=0.2MarginalUnitQuantityDiscountExampleStep1MarginalUnitQuantityDiscountExampleStep2Step3WhyQuantityDiscounts?QuantitydiscountscanincreasethesupplychainsurplusforthefollowingtwomainreasonsImprovedcoordinationtoincreasetotalsupplychainprofitsExtractionofsurplusthroughpricediscriminationQuantityDiscountsforCommodityProductsD=120,000bottles/year,SR

=$100,hR

=0.2,CR

=$3SM

=$250,hM

=0.2,CM

=$2Annualsupplychaincost(manufacturer+DO)=$6,009+$3,795=$9,804LocallyOptimalLotSizesAnnualcostforDOandmanufacturerAnnualsupplychaincost(manufacturer+DO)=$5,106+$4,059=$9,165DesigningaSuitableLotSize-BasedQuantityDiscountDesignasuitablequantitydiscountthatgetsDOtoorderinlotsof9,165unitswhenitsaimstominimizeonlyitsowntotalcostsManufacturerneedstoofferanincentiveofatleast$264peryeartoDOintermsofdecreasedmaterialcostifDOordersinlotsof9,165unitsAppropriatequantitydiscountis$3ifDOordersinlotssmallerthan9,165unitsand$2.9978forordersof9,165ormoreQuantityDiscountsWhen

FirmHasMarketPowerDemandcurve=360,000–60,000pProductioncost=CM=$2perbottleptomaximizeProfRQuantityDiscountsWhen

FirmHasMarketPowerCR=$4perbottle,p=$5perbottleTotalmarketdemand=360,000–60,000p=60,000ProfR

=(5–4)(360,000–60,000×5)=$60,000ProfM=(4–2)(360,000–60,000×5)=$120,000ProfSC=(p–CM)(360,000–60,000p)CoordinatedretailpriceProfSC=($4–$2)x120,000=$240,000Two-PartTariffManufacturerchargesitsentireprofitasanup-frontfranchisefeeff

SellstotheretaileratcostRetailpricingdecisionisbasedonmaximizingitsprofitsEffectivelymaximizesthecoordinatedsupplychainprofitVolume-BasedQuantityDiscountsDesignavolume-baseddiscountschemethatgetstheretailertopurchaseandsellthequantitysoldwhenthetwostagescoordinatetheiractionsLessonsfromDiscountingSchemesQuantitydiscountsplayaroleinsupplychaincoordinationandimprovedsupplychainprofitsDiscountschemesthatareoptimalarevolumebasedandnotlotsizebasedunlessthemanufacturerhaslargefixedcostsassociatedwitheachlotEveninthepresenceoflargefixedcostsforthemanufacturer,atwo-parttarifforvolume-baseddiscount,withthemanufacturerpassingonsomeofthefixedcosttotheretailer,optimallycoordinatesthesupplychainandmaximizesprofitsLessonsfromDiscountingSchemesLotsize–baseddiscountstendtoraisethecycleinventoryinthesupplychainVolume-baseddiscountsarecompatiblewithsmalllotsthatreducecycleinventoryRetailerswilltendtoincreasethesizeofthelottowardtheendoftheevaluationperiod,thehockeystickphenomenonWithmultipleretailerswithdifferentdemandcurves

optimaldiscountcontinuestobevolumebasedwiththeaveragepricechargedtotheretailersdecreasingastherateofpurchaseincreasesPriceDiscriminationtoMaximizeSupplierProfitsFirmchargesdifferentialpricestomaximizeprofitsSettingafixedpriceforallunitsdoesnotmaximizeprofitsforthemanufacturerManufacturercanobtainmaximumprofitsbypricingeachunitdifferentlybasedoncustomers’marginalevaluationateachquantityQuantitydiscountsareonemechanismforpricediscriminationbecausecustomerspaydifferentpricesbasedonthequantitypurchasedShort-TermDiscounting:

TradePromotionsTradepromotionsarepricediscountsforalimitedperiodoftimeKeygoalsInduceretailerstousepricediscounts,displays,oradvertisingtospursalesShiftinventoryfromthemanufacturertotheretailerandthecustomerDefendabrandagainstcompetitionShort-TermDiscounting:

TradePromotionsImpactonthebehavioroftheretailerandsupplychainperformanceRetailerhastwoprimaryoptionsPassthroughsomeorallofthepromotiontocustomerstospursalesPassthroughverylittleofthepromotiontocustomersbutpurchaseingreaterquantityduringthepromotionperiodtoexploitthetemporaryreductioninprice(forwardbuy)ForwardBuyingInventoryProfileFigure11-5ForwardBuyCoststobeconsidered–materialcost,holdingcost,andordercostThreeassumptionsThediscountisofferedonce,withnofuturediscountsTheretailertakesnoactiontoinfluencecustomerdemandAnalyzeaperiodoverwhichthedemandisanintegermultipleofQ*ForwardBuyOptimalorderquantityRetailersareoftenawareofthetimingofthenextpromotionImpactofTradePromotions

onLotSizesQ*=6,324bottles,C=$3perbottled=$0.15,D=120,000,h=0.2 CycleinventoryatDO =Q*/2=6,324/2=3,162bottles Averageflowtime =Q*/2D=6,324/(2D)=0.3162monthsImpactofTradePromotions

onLotSizes CycleinventoryatDO =Qd/2=38,236/2=19,118bottles Averageflowtime =Qd/2D=38,236/(20,000) =1.9118monthsWithtradepromotionsForwardbuy=Qd–Q*=38,236–6,324=31,912bottlesHowMuchofaDiscountShouldtheRetailerPassThrough?ProfitsfortheretailerProfR=(300,000–60,000p)p–(300,000–60,000p)CROptimalpricep=(300,000+60,000CR)/120,000DemandwithnopromotionDR=30,000–60,000p=60,000Optimalpricewithdiscountp=(300,000+60,000x2.85)/120,000=$3.925DR=300,000-60,000p=64,500DemandwithpromotionTradePromotionsTradepromotionsgenerallyincreasecycleinventoryinasupplychainandhurtperformanceCountermeasuresEDLP(everydaylowpricing)Discountappliestoitemssoldtocustomers(sell-through)notthequantitypurchasedbytheretailer(sell-in)ScanbasedpromotionsManagingMultiechelon

CycleInventoryMulti-echelonsupplychainshavemultiplestageswithpossiblymanyplayersateachstageLackofcoordinationinlotsizingdecisionsacrossthesupplychainresultsinhighcostsandmorecycleinventorythanrequiredThegoalistodecreasetotalcostsbycoordinatingordersacrossthesupplychainManagingMultiechelon

CycleInventoryFigure11-6IntegerReplenishmentPolicyDivideallpartieswithinastageintogroupssuchthatallpartieswithinagrouporderfromthesamesupplierandhaveth