供应链管理(第11、12讲)

Chapter7

ManagingEconomiesofScaleintheSupplyChain:CycleInventorySupplyChainManagement10-1OutlineRoleofCycleInventoryinaSupplyChainEconomiesofScaletoExploitFixedCostsEconomiesofScaletoExploitQuantityDiscountsShort-TermDiscounting:TradePromotionsEstimatingCycleInventory-RelatedCostsinPractice2第7章获取供应链规模经济的手段：循环库存一、循环库存在供应链中的作用二、利用固定成本获取规模经济三、利用数量折扣获取规模经济四、短期折扣：商业促销五、在实践中估测与循环库存相关的费用3循环库存产生原因——规模经济大批量生产与采购订购与运输数量折扣与促销4RoleofInventoryintheSupplyChainCostAvailabilityEfficiencyResponsiveness5RoleofCycleInventory

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

(Fig.7.1)Cycleinventory=Q/2(dependsdirectlyonlotsize)Averageflowtime=Avginventory/AvgflowrateAverageflowtimefromcycleinventory=Q/(2D)6RoleofCycleInventory

inaSupplyChainQ=1000unitsD=100units/dayCycleinventory=Q/2=1000/2=500=AvginventorylevelfromcycleinventoryAvgflowtime=Q/2D=1000/(2)(100)=5daysCycleinventoryadds5daystothetimeaunitspendsinthesupplychainLowercycleinventoryisbetterbecause:AverageflowtimeislowerWorkingcapitalrequirementsarelowerLowerinventoryholdingcosts7RoleofCycleInventory

inaSupplyChainCycleinventoryisheldprimarilytotakeadvantageofeconomiesofscaleinthesupplychainSupplychaincostsinfluencedbylotsize:Materialcost=CFixedorderingcost=SHoldingcost=H=hC(h=costofholding$1ininventoryforoneyear)Primaryroleofcycleinventoryistoallowdifferentstagestopurchaseproductinlotsizesthatminimizethesumofmaterial,ordering,andholdingcostsIdeally,cycleinventorydecisionsshouldconsidercostsacrosstheentiresupplychain,butinpractice,eachstagegenerallymakesitsownsupplychaindecisions–increasestotalcycleinventoryandtotalcostsinthesupplychain8循环库存在供应链中的作用循环库存指供应链中建立的平均库存量Q：订购批量R：单位时间需求量（假设需求量不变）循环库存＝批量库存/2＝Q/2循环库存平均周转时间＝循环库存/需求量＝Q/2R为减少市场波动，公司理想循环库存一般较小TQ9EconomiesofScale

toExploitFixedCostsHowdoyoudecidewhethertogoshoppingataconveniencestoreoratSam’sClub?Lotsizingforasingleproduct(EOQ)10EconomiesofScale

toExploitFixedCostsAnnualdemand=DNumberofordersperyear=D/QAnnualmaterialcost=CDAnnualordercost=(D/Q)SAnnualholdingcost=(Q/2)H=(Q/2)hCTotalannualcost=TC=CD+(D/Q)S+(Q/2)hCFigure7.2showsvariationindifferentcostsfordifferentlotsizes11FixedCosts:OptimalLotSize

andReorderInterval(EOQ)

D: AnnualdemandS: SetuporOrderCostC: Costperunith: HoldingcostperyearasafractionofproductcostH: HoldingcostperunitperyearQ: LotSizeT: ReorderintervalMaterialcostisconstantandthereforeisnotconsideredinthismodel12利用固定成本获取规模经济单一产品批量规模Q（经济订购批量）R＝产品年需求量S＝每次订购固定成本C＝单位产品购买价格成本H＝每年存储成本年原料价格成本＝CR年订购次数＝R/Q年订购成本＝（R/Q）*S年存储成本＝（Q/2）H=(Q/2)hc年总成本TC＝CR+（R/Q）*S+（Q/2）hc13年总成本TC＝CR+（R/Q）*S+（Q/2）hc等式右边对q一阶求导，等于0时，得最佳订购批量Q*=注：h和R必须要有相同时间单位n＝R/Q*＝14批量规模成本总成本储存成本订购成本原材料成本Q*15Example7.1Demand,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=0.98month16Example7.1(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,thefixedcostassociatedwitheachlotwouldhavetobereduced17Example7.2Ifdesiredlotsize=Q*=200units,whatwouldShave

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

18例：bestbuy公司采购电脑，月需求1000台，固定成本每次4000，进价每台500，零售商库存成本占20％，求Q*解：年需求量R=1000*12=12000每批订购成本S=4000单位采购成本C=500年存储成本h＝0.2Q*=（（2*12000*4000）/（0.2*500））1/2＝980循环库存＝Q*/2=490年订购次数＝R/Q*=120000/980=12.24订购和存储成本＝（R/Q*）S+（Q*/2）hC=97980平均周转时间＝Q*/2R=490/1200=0.041年＝0.49月19拓展：A、如果批量规模1100，而不是980，则：订购次数＝12000/1100＝10.9总成本＝10.9*4000+1100/2*0.2*500＝43600+55000＝98600批量规模从980到1100，增加10％，总成本从97980到98600，仅增加0.6％。20B、假设月需求增加到4000每月（增长4倍），最佳规模批量和订购次数各自增加2倍，平均周转时间减少至1/2。Q*=年订购次数＝R/Q*平均周转时间＝Q*/2R结论：如果批量规模最佳，需求量增加，循环库存周转时间会减少。21C、如果批量规模为200，则：年库存成本＝（R/Q）*S+(Q/2)hC＝（12*1000/200）*4000+（200/2）0.2*500=250000>>97980为了减少批量规模，只能减少固定成本。如果期望批量规模为200，则Q*=S=(hC(Q*）2)/(2*R)=0.2*500*200*200/(2*12000)=166.7<<400022KeyPointsfromEOQModelIndecidingtheoptimallotsize,thetradeoffisbetweensetup(order)costandholdingcost.Ifdemandincreasesbyafactorof4,itisoptimaltoincreasebatchsizebyafactorof2andproduce(order)twiceasoften.Cycleinventory(indaysofdemand)shoulddecreaseasdemandincreases.Iflotsizeistobereduced,onehastoreducefixedordercost.Toreducelotsizebyafactorof2,ordercosthastobereducedbyafactorof4.23EconomiesofScaleto

ExploitQuantityDiscountsAll-unitquantitydiscountsMarginalunitquantitydiscountsWhyquantitydiscounts?CoordinationinthesupplychainPricediscriminationtomaximizesupplierprofits24QuantityDiscountsLotsizebasedAllunitsMarginalunitVolumebasedHowshouldbuyerreact?Whatareappropriatediscountingschemes?25All-UnitQuantityDiscountsPricingschedulehasspecifiedquantitybreakpointsq0,q1,…,qr,whereq0=0Ifanorderisplacedthatisatleastaslargeasqibutsmallerthanqi+1,theneachunithasanaverageunitcostofCiTheunitcostgenerallydecreasesasthequantityincreases,i.e.,C0>C1>…>Cr

Theobjectiveforthecompany(aretailerinourexample)istodecideonalotsizethatwillminimizethesumofmaterial,order,andholdingcosts26All-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.27All-UnitQuantityDiscounts:ExampleCost/Unit$3$2.96$2.92OrderQuantity5,00010,000OrderQuantity5,00010,000TotalMaterialCost28All-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=0.229All-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=1000130All-UnitQuantityDiscountsSupposefixedordercostwerereducedto$4Withoutdiscount,Q*wouldbereducedto1265unitsWithdiscount,optimallotsizewouldstillbe10001unitsWhatistheeffectofsuchadiscountschedule?RetailersareencouragedtoincreasethesizeoftheirordersAverageinventory(cycleinventory)inthesupplychainisincreasedAverageflowtimeisincreasedIsanall-unitquantitydiscountanadvantageinthesupplychain?31利用数量折扣获取规模经济全部单位数量折扣qi<Qi<qi+1TCi＝（R/Qi）S+(Qi/2)+RCi32月需求量1000订购成本100储存成本20%订购数量单价0-500035001-100002.9610000-2.92Drugonline33解：q0＝0，q1＝5000，q2＝10000C0＝3，C1＝2.96，C2＝2.92R=120000,S=100,h＝0.2Q0*=(2RS/hC)1/2

＝(2*120000*100/3*0.2)1/2

＝6324q1＝5000时，TC0=(R/q1)S+(q1/2)hC1+RC1=120000/5000*100+5000/2*0.2*2.96+120000*2.96＝359080Q1*=(2RS/hC)1/2

＝(2*12000*100/2.96*0.2)1/2

＝6367Q1*=6367时，TC1=(R/Q1)S+(Q1/2)hC+RC1=358969Q2*=(2RS/hC)1/2

＝(2*12000*100/3*0.2)1/2

＝6410q2=10000时，TC2=(R/q2)S+(q1/2)hC+RC1=35452034WhyQuantityDiscounts?CoordinationinthesupplychainCommodityproductsProductswithdemandcurve2-parttariffsVolumediscounts35Coordinationfor

CommodityProductsD=120,000bottles/yearSR=$100,hR=0.2,CR=$3SS=$250,hS=0.2,CS=$2Retailer’soptimallotsize=6,324bottlesRetailercost=$3,795;Suppliercost=$6,009Supplychaincost=$9,80436Coordinationfor

CommodityProductsWhatcanthesupplierdotodecreasesupplychaincosts?Coordinatedlotsize:9,165;Retailercost=$4,059;Suppliercost=$5,106;Supplychaincost=$9,165EffectivepricingschemesAll-unitquantitydiscount$3forlotsbelow9,165$2.9978forlotsof9,165ormorePasssomefixedcosttoretailer(enoughthatheraisesordersizefrom6,324to9,165)37QuantityDiscountsWhen

FirmHasMarketPowerNoinventoryrelatedcostsDemandcurve 360,000-60,000pWhataretheoptimalpricesandprofitsinthefollowingsituations?ThetwostagescoordinatethepricingdecisionPrice=$4,Profit=$240,000,Demand=120,000ThetwostagesmakethepricingdecisionindependentlyPrice=$5,Profit=$180,000,Demand=60,00038Two-PartTariffsand

VolumeDiscountsDesignatwo-parttariffthatachievesthecoordinatedsolutionDesignavolumediscountschemethatachievesthecoordinatedsolutionImpactofinventorycostsPassonsomefixedcostswithabovepricing39LessonsfromDiscountingSchemesLotsizebaseddiscountsincreaselotsizeandcycleinventoryinthesupplychainLotsizebaseddiscountsarejustifiedtoachievecoordinationforcommodityproductsVolumebaseddiscountswithsomefixedcostpassedontoretaileraremoreeffectiveingeneralVolumebaseddiscountsarebetteroverrollinghorizon40为什么采取数量折扣的策略1）供应链的协调如果供应链是纵向一体化，且每一阶段运作均考虑供应链总体利润，则可以实现协调运作，但是，产权的差异，导致各阶段追求各自利益最大化。41A、对最终产品数量折扣——案例Vitaminco：R＝10000，S＝100，h＝20％，Cm＝3；计算出Q*＝6324，TC＝3795制造商：S＝250，C0＝2，h＝20％。制造商订购成本＝120000/6324*250＝4744制造商年存储成本＝6324/2*2*0.2＝1265总成本＝4744+1265＝6009供应链总成本＝6009+3795＝9804如果Q*＝9165，则：供应链总成本＝120000/9165*100+9165/2*3*0.2+120000/9165*250+9165/2*2*0.2＝4059+5106＝9165结论：制造商会通过数量折扣让度部分利益，实现总体利益最大化42引论：以批量折扣为基础的折扣降低了供应链总成本，但增加了零售商采购批量，增加了供应链循环库存。如果制造商致力于降低其建设成本和订购成本时，规模折扣就会发生改变。但实际情况却是，生产运作部门降低固定成本，营销部门提供数量折扣？！（思考）43B、对公司有市场控制权的产品实行数量折扣案例：某药品市场需求曲线q=360000-60000p。制造商成本c0=2，批发价c1=4。r销=（360000-60000p）p-（360000-60000p）c1r`=360000-120000p+60000c1=0P=5q=60000r销=60000r制=120000r供=18000整合后：p=4q=120000r供=18000044协调方法：第一种、两部分定价：制造商先索取全部利润作为前期特许经营费，再将产品以成本出售第二种、以总量为基础的数量折扣Q<12000,p=4；Q>12000,p=3.5注意：零售商在期末加大采购，即曲棍球现象。对策：将总量折扣建立在滚动水平基础上（以过去12周或者90天销售量为基础）452）利用差别定价使供应链利润最大化顾客剩余厂商收益需求曲线供给曲线46Short-TermDiscounting:

TradePromotionsTradepromotionsarepricediscountsforalimitedperiodoftime(alsomayrequirespecificactionsfromretailers,suchasdisplays,advertising,etc.)Keygoalsforpromotionsfromamanufacturer’sperspective:Induceretailerstousepricediscounts,displays,advertisingtoincreasesalesShiftinventoryfromthemanufacturertotheretailerandcustomerDefendabrandagainstcompetitionGoalsarenotalwaysachievedbyatradepromotionWhatistheimpactonthebehavioroftheretailerandontheperformanceofthesupplychain?Retailerhastwoprimaryoptionsinresponsetoapromotion:PassthroughsomeorallofthepromotiontocustomerstospursalesPurchaseingreaterquantityduringpromotionperiodtotakeadvantageoftemporarypricereduction,butpassthroughverylittleofsavingstocustomers47ShortTermDiscountingQ*:NormalorderquantityC:Normalunitcostd:ShorttermdiscountD:Annualdemandh:Costofholding$1peryearQd:ShorttermorderquantityForwardbuy=Qd-Q*48ShortTermDiscounts:

ForwardBuyingNormalordersize,Q*=6,324bottlesNormalcost,C=$3perbottleDiscountpertube,d=$0.15Annualdemand,D=120,000Holdingcost,h=0.2Qd=Forwardbuy=49PromotionPassThrough

toConsumersDemandcurveatretailer:300,000-60,000pNormalsupplierprice,CR=$3.00Optimalretailprice=$4.00Customerdemand=60,000Promotiondiscount=$0.15Optimalretailprice=$3.925Customerdemand=64,500Retaileronlypassesthroughhalfthepromotiondiscountanddemandincreasesbyonly7.5%50TradePromotionsWhenamanufactureroffersapromotion,thegoalforthemanufactureristotakeactions(countermeasures)todiscourageforwardbuyinginthesupplychainCountermeasuresEDLPScanbasedpromotionsCustomercoupons51短期折扣：商业促销制造商目的：引导零售商通过价格折扣、展示或者广告宣传刺激销售；制造商库存转移；品牌竞争经销商选择：将一部分或者全部促销优惠让度给消费者，刺激销售；只是让度一小部分，大批购进，缓慢销售。52折扣价格下的最优订购数量：假设：折扣仅提供一次；Qd是Q*的倍数；零售商不将优惠让度给顾客。Qd＝dR/（C-d）h+CQ*/(C-d)超前采购量＝Qd-Q*如果零售商知道下一个促销时间，设为Q1，则会选择Q1和Qd的最小值。53案例：DO公司R=120000,CM=3,h＝0.2，Q*=6324,d＝0.15，求零售商订购数量？

Qd＝dR/（C-d）h+CQ*/(C-d)＝0.15*120000/（3-0.15）0.2+3*6324/（3-0.15）＝38236循环库存＝19118平均周转时间＝38236/2*1