Chapter10

ManagingEconomiesofScaleintheSupplyChain:CycleInventorySupplyChainManagement

(3rdEdition)

10-1OutlineRoleofCycleInventoryinaSupplyChainEconomiesofScaletoExploitFixedCostsEconomiesofScaletoExploitQuantityDiscountsShort-TermDiscounting:TradePromotionsManagingMulti-EchelonCycleInventoryEstimatingCycleInventory-RelatedCostsinPractice2RoleofInventoryintheSupplyChainCostAvailabilityEfficiencyResponsiveness3RoleofCycleInventory

inaSupplyChainLot,orbatchsize:quantitythatasupplychainstageeitherproducesorordersatagiventimeCycleinventory:averageinventorythatbuildsupinthesupplychainbecauseasupplychainstageeitherproducesorpurchasesinlotsthatarelargerthanthosedemandedbythecustomerQ=lotorbatchsizeofanorderD=demandperunittimeInventoryprofile:plotoftheinventorylevelovertime

(Fig.10.1)Cycleinventory=Q/2(dependsdirectlyonlotsize)Averageflowtime=Avginventory/AvgflowrateAverageflowtimefromcycleinventory=Q/(2D)4RoleofCycleInventory

inaSupplyChainQ=1000unitsD=100units/dayCycleinventory=Q/2=1000/2=500=AvginventorylevelfromcycleinventoryAvgflowtime=Q/2D=1000/(2)(100)=5daysCycleinventoryadds5daystothetimeaunitspendsinthesupplychainLowercycleinventoryisbetterbecause:AverageflowtimeislowerWorkingcapitalrequirementsarelowerLowerinventoryholdingcosts5RoleofCycleInventory

inaSupplyChainCycleinventoryisheldprimarilytotakeadvantageofeconomiesofscaleinthesupplychainSupplychaincostsinfluencedbylotsize:Materialcost=CFixedorderingcost=SHoldingcost=H=hC(h=costofholding$1ininventoryforoneyear)Primaryroleofcycleinventoryistoallowdifferentstagestopurchaseproductinlotsizesthatminimizethesumofmaterial,ordering,andholdingcostsIdeally,cycleinventorydecisionsshouldconsidercostsacrosstheentiresupplychain,butinpractice,eachstagegenerallymakesitsownsupplychaindecisions–increasestotalcycleinventoryandtotalcostsinthesupplychain6EconomiesofScale

toExploitFixedCostsHowdoyoudecidewhethertogoshoppingataconveniencestoreoratSam’sClub?Lotsizingforasingleproduct(EOQ)AggregatingmultipleproductsinasingleorderLotsizingwithmultipleproductsorcustomersLotsareorderedanddeliveredindependentlyforeachproductLotsareorderedanddeliveredjointlyforallproductsLotsareorderedanddeliveredjointlyforasubsetofproducts7EconomiesofScale

toExploitFixedCostsAnnualdemand=DNumberofordersperyear=D/QAnnualmaterialcost=CRAnnualordercost=(D/Q)SAnnualholdingcost=(Q/2)H=(Q/2)hCTotalannualcost=TC=CD+(D/Q)S+(Q/2)hCFigure10.2showsvariationindifferentcostsfordifferentlotsizes8FixedCosts:OptimalLotSize

andReorderInterval(EOQ)

D: AnnualdemandS: SetuporOrderCostC: Costperunith: HoldingcostperyearasafractionofproductcostH: HoldingcostperunitperyearQ: LotSizeT: ReorderintervalMaterialcostisconstantandthereforeisnotconsideredinthismodel9Example10.1Demand,D=12,000computersperyeard=1000computers/monthUnitcost,C=$500Holdingcostfraction,h=0.2Fixedcost,S=$4,000/orderQ*=Sqrt[(2)(12000)(4000)/(0.2)(500)]=980computersCycleinventory=Q/2=490Flowtime=Q/2d=980/(2)(1000)=0.49monthReorderinterval,T=0.98month10Example10.1(continued)Annualorderingandholdingcost==(12000/980)(4000)+(980/2)(0.2)(500)=$97,980SupposelotsizeisreducedtoQ=200,whichwouldreduceflowtime:Annualorderingandholdingcost==(12000/200)(4000)+(200/2)(0.2)(500)=$250,000Tomakeiteconomicallyfeasibletoreducelotsize,thefixedcostassociatedwitheachlotwouldhavetobereduced11Example10.2Ifdesiredlotsize=Q*=200units,whatwouldShave

tobe?D=12000unitsC=$500h=0.2UseEOQequationandsolveforS:S =[hC(Q*)2]/2D=[(0.2)(500)(200)2]/(2)(12000)=$166.67Toreduceoptimallotsizebyafactorofk,thefixedordercostmustbereducedbyafactorofk2

12KeyPointsfromEOQModelIndecidingtheoptimallotsize,thetradeoffisbetweensetup(order)costandholdingcost.Ifdemandincreasesbyafactorof4,itisoptimaltoincreasebatchsizebyafactorof2andproduce(order)twiceasoften.Cycleinventory(indaysofdemand)shoulddecreaseasdemandincreases.Iflotsizeistobereduced,onehastoreducefixedordercost.Toreducelotsizebyafactorof2,ordercosthastobereducedbyafactorof4.13AggregatingMultipleProducts

inaSingleOrderTransportationisasignificantcontributortothefixedcostperorderCanpossiblycombineshipmentsofdifferentproductsfromthesamesuppliersameoverallfixedcostsharedovermorethanoneproducteffectivefixedcostisreducedforeachproductlotsizeforeachproductcanbereducedCanalsohaveasingledeliverycomingfrommultiplesuppliersorasingletruckdeliveringtomultipleretailersAggregatingacrossproducts,retailers,orsuppliersinasingleorderallowsforareductioninlotsizeforindividualproductsbecausefixedorderingandtransportationcostsarenowspreadacrossmultipleproducts,retailers,orsuppliers14Example:AggregatingMultipleProductsinaSingleOrderSupposethereare4computerproductsinthepreviousexample:Deskpro,Litepro,Medpro,andHeavproAssumedemandforeachis1000unitspermonthIfeachproductisorderedseparately:Q*=980unitsforeachproductTotalcycleinventory=4(Q/2)=(4)(980)/2=1960unitsAggregateordersofallfourproducts:CombinedQ*=1960unitsForeachproduct:Q*=1960/4=490Cycleinventoryforeachproductisreducedto490/2=245Totalcycleinventory=1960/2=980unitsAverageflowtime,inventoryholdingcostswillbereduced15LotSizingwithMultiple

ProductsorCustomersInpractice,thefixedorderingcostisdependentatleastinpartonthevarietyassociatedwithanorderofmultiplemodelsAportionofthecostisrelatedtotransportation(independentofvariety)Aportionofthecostisrelatedtoloadingandreceiving(notindependentofvariety)Threescenarios:LotsareorderedanddeliveredindependentlyforeachproductLotsareorderedanddeliveredjointlyforallthreemodelsLotsareorderedanddeliveredjointlyforaselectedsubsetofmodels16LotSizingwithMultipleProductsDemandperyearDL=12,000;DM=1,200;DH=120Commontransportationcost,S=$4,000ProductspecificordercostsL=$1,000;sM=$1,000;sH=$1,000Holdingcost,h=0.2UnitcostCL=$500;CM=$500;CH=$50017DeliveryOptionsNoAggregation:EachproductorderedseparatelyCompleteAggregation:AllproductsdeliveredoneachtruckTailoredAggregation:Selectedsubsetsofproductsoneachtruck18NoAggregation:OrderEachProductIndependentlyTotalcost=$155,14019Aggregation:OrderAll

ProductsJointlyS*=S+sL+sM+sH=4000+1000+1000+1000=$7000n*=Sqrt[(DLhCL+DMhCM+DHhCH)/2S*]=9.75QL=DL/n*=12000/9.75=1230QM=DM/n*=1200/9.75=123QH=DH/n*=120/9.75=12.3Cycleinventory=Q/2Averageflowtime=(Q/2)/(weeklydemand)20CompleteAggregation:

OrderAllProductsJointlyAnnualordercost=9.75×$7,000=$68,250Annualtotalcost=$136,52821LessonsfromAggregationAggregationallowsfirmtolowerlotsizewithoutincreasingcostCompleteaggregationiseffectiveifproductspecificfixedcostisasmallfractionofjointfixedcostTailoredaggregationiseffectiveifproductspecificfixedcostisalargefractionofjointfixedcost22EconomiesofScaleto

ExploitQuantityDiscountsAll-unitquantitydiscountsMarginalunitquantitydiscountsWhyquantitydiscounts?CoordinationinthesupplychainPricediscriminationtomaximizesupplierprofits23QuantityDiscountsLotsizebasedAllunitsMarginalunitVolumebasedHowshouldbuyerreact?Whatareappropriatediscountingschemes?24All-UnitQuantityDiscountsPricingschedulehasspecifiedquantitybreakpointsq0,q1,…,qr,whereq0=0Ifanorderisplacedthatisatleastaslargeasqibutsmallerthanqi+1,theneachunithasanaverageunitcostofCiTheunitcostgenerallydecreasesasthequantityincreases,i.e.,C0>C1>…>Cr

Theobjectiveforthecompany(aretailerinourexample)istodecideonalotsizethatwillminimizethesumofmaterial,order,andholdingcosts25All-UnitQuantityDiscountProcedure(differentfromwhatisinthetextbook)Step1:CalculatetheEOQforthelowestprice.Ifitisfeasible(i.e.,thisorderquantityisintherangeforthatprice),thenstop.Thisistheoptimallotsize.CalculateTCforthislotsize.Step2:IftheEOQisnotfeasible,calculatetheTCforthispriceandthesmallestquantityforthatprice.Step3:CalculatetheEOQforthenextlowestprice.Ifitisfeasible,stopandcalculatetheTCforthatquantityandprice.Step4:ComparetheTCforSteps2and3.ChoosethequantitycorrespondingtothelowestTC.Step5:IftheEOQinStep3isnotfeasible,repeatSteps2,3,and4untilafeasibleEOQisfound.26All-UnitQuantityDiscounts:ExampleCost/Unit$3$2.96$2.92OrderQuantity5,00010,000OrderQuantity5,00010,000TotalMaterialCost27All-UnitQuantityDiscount:ExampleOrderquantity UnitPrice0-5000 $3.005001-10000 $2.96Over10000 $2.92q0=0,q1=5000,q2=10000C0=$3.00,C1=$2.96,C2=$2.92D=120000units/year,S=$100/lot,h=0.228All-UnitQuantityDiscount:ExampleStep1:CalculateQ2*=Sqrt[(2DS)/hC2]=Sqrt[(2)(120000)(100)/(0.2)(2.92)]=6410Notfeasible(6410<10001)CalculateTC2usingC2=$2.92andq2=10001TC2=(120000/10001)(100)+(10001/2)(0.2)(2.92)+(120000)(2.92)=$354,520Step2:CalculateQ1*=Sqrt[(2DS)/hC1]=Sqrt[(2)(120000)(100)/(0.2)(2.96)]=6367Feasible(5000<6367<10000)

StopTC1=(120000/6367)(100)+(6367/2)(0.2)(2.96)+(120000)(2.96)=$358,969TC2<TC1

TheoptimalorderquantityQ*isq2=1000129All-UnitQuantityDiscountsSupposefixedordercostwerereducedto$4Withoutdiscount,Q*wouldbereducedto1265unitsWithdiscount,optimallotsizewouldstillbe10001unitsWhatistheeffectofsuchadiscountschedule?RetailersareencouragedtoincreasethesizeoftheirordersAverageinventory(cycleinventory)inthesupplychainisincreasedAverageflowtimeisincreasedIsanall-unitquantitydiscountanadvantageinthesupplychain?30WhyQuantityDiscounts?CoordinationinthesupplychainCommodityproductsProductswithdemandcurve2-parttariffsVolumediscounts31Coordinationfor

CommodityProductsD=120,000bottles/yearSR=$100,hR=0.2,CR=$3SS=$250,hS=0.2,CS=$2Retailer’soptimallotsize=6,324bottlesRetailercost=$3,795;Suppliercost=$6,009Supplychaincost=$9,80432Coordinationfor

CommodityProductsWhatcanthesupplierdotodecreasesupplychaincosts?Coordinatedlotsize:9,165;Retailercost=$4,059;Suppliercost=$5,106;Supplychaincost=$9,165EffectivepricingschemesAll-unitquantitydiscount$3forlotsbelow9,165$2.9978forlotsof9,165ormorePasssomefixedcosttoretailer(enoughthatheraisesordersizefrom6,324to9,165)33QuantityDiscountsWhen

FirmHasMarketPowerNoinventoryrelatedcostsDemandcurve 360,000-60,000pWhataretheoptimalpricesandprofitsinthefollowingsituations?ThetwostagescoordinatethepricingdecisionPrice=$4,Profit=$240,000,Demand=120,000ThetwostagesmakethepricingdecisionindependentlyPrice=$5,Profit=$180,000,Demand=60,00034Two-PartTariffsand

VolumeDiscountsDesignatwo-parttariffthatachievesthecoordinatedsolutionDesignavolumediscountschemethatachievesthecoordinatedsolutionImpactofinventorycostsPassonsomefixedcostswithabovepricing35LessonsfromDiscountingSchemesLotsizebaseddiscountsincreaselotsizeandcycleinventoryinthesupplychainLotsizebaseddiscountsarejustifiedtoachievecoordinationforcommodityproductsVolumebaseddiscountswithsomefixedcostpassedontoretaileraremoreeffectiveingeneralVolumebaseddiscountsarebetteroverrollinghorizon36Short-TermDiscounting:

TradePromotionsTradepromotionsarepricediscountsforalimitedperiodoftime(alsomayrequirespecificactionsfromretailers,suchasdisplays,advertising,etc.)Keygoalsforpromotionsfromamanufacturer’sperspective:Induceretailerstousepricediscounts,displays,advertisingtoincreasesalesShiftinventoryfromthemanufacturertotheretailerandcustomerDefendabrandagainstcompetitionGoalsarenotalwaysachievedbyatradepromotionWhatistheimpactonthebehavioroftheretailerandontheperformanceofthesupplychain?Retailerhastwoprimaryoptionsinresponsetoapromotion:PassthroughsomeorallofthepromotiontocustomerstospursalesPurchaseingreaterquantityduringpromotionperiodtotakeadvantageoftemporarypricereduction,butpassthroughverylittleofsavingstocustomers37ShortTermDiscountingQ*:NormalorderquantityC:Normalunitcostd:ShorttermdiscountD:Annualdemandh:Costofholding$1peryearQd:ShorttermorderquantityForwardbuy=Qd-Q*38ShortTermDiscounts:

ForwardBuyingNormalordersize,Q*=6,324bottlesNormalcost,C=$3perbottleDiscountpertube,d=$0.15Annualdemand,D=120,000Holdingcost,h=0.2Qd=Forwardbuy=39PromotionPassThrough

toConsumersDemandcurveatretailer:300,000-60,000pNormalsupplierprice,CR=$3.00Optimalretailprice=$4.00Customerdemand=60,000Promotiondiscount=$0.15Optimalretailprice=$3.925Customerdemand=64,500Retaileronlypassesthroughhalfthepromotiondiscountanddemandincreasesbyonly7.5%40TradePromotionsWhenamanufactureroffersapromotion,thegoalforthemanufactureristotakeactions(countermeasures)todiscourageforwardbuyinginthesupplychainCountermeasuresEDLPScanbasedpromotionsCustomercoupons41ManagingMulti-Echelon

CycleInventoryMulti-echelonsupplychainshavemultiplestages,withpossiblymanyplayersateachstageandonestagesupplyinganotherstageThegoalistosynchronizelotsizesatdifferentstages