1、 2007 Pearson EducationChapter 7Managing Economies of Scale in the Supply Chain:Cycle InventorySupply Chain Management10-1 2007 Pearson EducationOutlineuRole of Cycle Inventory in a Supply ChainuEconomies of Scale to Exploit Fixed CostsuEconomies of Scale to Exploit Quantity DiscountsuShort-Term Dis
2、counting:Trade PromotionsuEstimating Cycle Inventory-Related Costs in Practice2 2007 Pearson Education第第7 7章章 获取供应链规模经济的手段：获取供应链规模经济的手段：循环库存循环库存u一、循环库存在供应链中的作用u二、利用固定成本获取规模经济u三、利用数量折扣获取规模经济u四、短期折扣：商业促销u五、在实践中估测与循环库存相关的费用3 2007 Pearson Education循环库存产生原因循环库存产生原因u规模经济u大批量生产与采购u订购与运输u数量折扣与促销4 2007 Pears
3、on EducationRole of Inventory in the Supply ChainImprove Matching of Supplyand DemandImproved ForecastingReduce Material Flow TimeReduce Waiting TimeReduce Buffer InventoryEconomies of ScaleSupply/DemandVariabilitySeasonalVariabilityCycle InventorySafety InventorySeasonal Inventory5 2007 Pearson Edu
4、cationRole of Cycle Inventoryin a Supply ChainuLot,or batch size:quantity that a supply chain stage either produces or orders at a given timeuCycle inventory:average inventory that builds up in the supply chain because a supply chain stage either produces or purchases in lots that are larger than th
5、ose demanded by the customer Q=lot or batch size of an order D=demand per unit timeuInventory profile:plot of the inventory level over time(Fig.7.1)uCycle inventory=Q/2(depends directly on lot size)uAverage flow time=Avg inventory/Avg flow rateuAverage flow time from cycle inventory=Q/(2D)6 2007 Pea
6、rson EducationRole of Cycle Inventoryin a Supply ChainQ=1000 unitsD=100 units/dayCycle inventory=Q/2=1000/2=500=Avg inventory level from cycle inventoryAvg flow time=Q/2D=1000/(2)(100)=5 daysuCycle inventory adds 5 days to the time a unit spends in the supply chainuLower cycle inventory is better be
7、cause:Average flow time is lower Working capital requirements are lower Lower inventory holding costs7 2007 Pearson EducationRole of Cycle Inventoryin a Supply ChainuCycle inventory is held primarily to take advantage of economies of scale in the supply chainuSupply chain costs influenced by lot siz
8、e:Material cost=C Fixed ordering cost=S Holding cost=H=hC(h=cost of holding$1 in inventory for one year)uPrimary role of cycle inventory is to allow different stages to purchase product in lot sizes that minimize the sum of material,ordering,and holding costsuIdeally,cycle inventory decisions should
9、 consider costs across the entire supply chain,but in practice,each stage generally makes its own supply chain decisions increases total cycle inventory and total costs in the supply chain8 2007 Pearson Education循环库存在供应链中的作用循环库存在供应链中的作用u循环库存指供应链中建立的平均库存量uQ：订购批量uR：单位时间需求量（假设需求量不变）u循环库存批量库存/2Q/2u循环库存平
10、均周转时间循环库存/需求量Q/2Ru为减少市场波动，公司理想循环库存一般较小TQ9 2007 Pearson EducationEconomies of Scaleto Exploit Fixed CostsuHow do you decide whether to go shopping at a convenience store or at Sams Club?uLot sizing for a single product(EOQ)10 2007 Pearson EducationEconomies of Scaleto Exploit Fixed CostsAnnual demand
11、=DNumber of orders per year=D/QAnnual material cost=CDAnnual order cost=(D/Q)SAnnual holding cost=(Q/2)H=(Q/2)hCTotal annual cost=TC=CD+(D/Q)S+(Q/2)hCFigure 7.2 shows variation in different costs for different lot sizes11 2007 Pearson EducationFixed Costs:Optimal Lot Sizeand Reorder Interval(EOQ)D:A
12、nnual demand S:Setup or Order CostC:Cost per unith:Holding cost per year as a fraction of product costH:Holding cost per unit per yearQ:Lot SizeT:Reorder intervalMaterial cost is constant and therefore is not considered in this modelDHSnHDSQhCH2*2*12 2007 Pearson Education利用固定成本获取规模经济利用固定成本获取规模经济u单一
13、产品批量规模Q（经济订购批量）uR产品年需求量uS每次订购固定成本uC单位产品购买价格成本uH每年存储成本u年原料价格成本CRu年订购次数R/Qu年订购成本（R/Q）*Su年存储成本（Q/2）H=(Q/2)hcu年总成本TC CR+（R/Q）*S+（Q/2）hc13 2007 Pearson Educationu年总成本TC CR+（R/Q）*S+（Q/2）hcu等式右边对q一阶求导，等于0时，得最佳订购批量uQ*=u注：h和R必须要有相同时间单位unR/Q*2RChS2RSCh14 2007 Pearson Education批量规模成本总成本储存成本订购成本原材料成本Q*15 2007 P
14、earson EducationExample 7.1Demand,D=12,000 computers per yeard=1000 computers/monthUnit cost,C=$500Holding cost fraction,h=0.2Fixed cost,S=$4,000/orderQ*=Sqrt(2)(12000)(4000)/(0.2)(500)=980 computers Cycle inventory=Q/2=490Flow time=Q/2d=980/(2)(1000)=0.49 monthReorder interval,T=0.98 month16 2007 P
15、earson EducationExample 7.1(continued)Annual ordering and holding cost=(12000/980)(4000)+(980/2)(0.2)(500)=$97,980Suppose lot size is reduced to Q=200,which would reduce flow time:Annual ordering and holding cost=(12000/200)(4000)+(200/2)(0.2)(500)=$250,000To make it economically feasible to reduce
16、lot size,the fixed cost associated with each lot would have to be reduced17 2007 Pearson EducationExample 7.2If desired lot size=Q*=200 units,what would S haveto be?D=12000 unitsC=$500h=0.2Use EOQ equation and solve for S:S=hC(Q*)2/2D=(0.2)(500)(200)2/(2)(12000)=$166.67To reduce optimal lot size by
17、a factor of k,the fixed order cost must be reduced by a factor of k2 18 2007 Pearson Education例：例：best buybest buy公司采购电脑，月需求公司采购电脑，月需求10001000台，固定成本每次台，固定成本每次40004000，进价，进价每台每台500500，零售商库存成本占，零售商库存成本占2020，求，求Q Q*u解：年需求量R=1000*12=12000u每批订购成本S=4000u单位采购成本C=500u年存储成本h0.2uQ*=（2*12000*4000）/（0.2*500）1/2
18、980u循环库存Q*/2=490u年订购次数R/Q*=120000/980=12.24u订购和存储成本（R/Q*）S+（Q*/2）hC=97980u平均周转时间Q*/2R=490/1200=0.041年0.49月19 2007 Pearson Educationu拓展：uA、如果批量规模1100，而不是980，则：u订购次数12000/110010.9u总成本10.9*4000+1100/2*0.2*50043600+5500098600u批量规模从980到1100，增加10，总成本从97980到98600，仅增加0.6。20 2007 Pearson EducationuB、假设月需求增加到
19、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。uQ*=u年订购次数R/Q*u平均周转时间Q*/2Ru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。21 2007 Pearson EducationuC、如果批量规模为200，则：u年库存成本u（R/Q）*S+(Q/2)hCu（12*1000/200）*4000+（200/2）0.2*500u=250000 97980u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uQ*=uS=(hC(Q*）2)/(2*R)u=0.2*500*200*200/(2*12000)=166.7
20、C1Cr uThe objective for the company(a retailer in our example)is to decide on a lot size that will minimize the sum of material,order,and holding costs26 2007 Pearson EducationAll-Unit Quantity Discount Procedure(different from what is in the textbook)Step 1:Calculate the EOQ for the lowest price.If
21、 it is feasible(i.e.,this order quantity is in the range for that price),then stop.This is the optimal lot size.Calculate TC for this lot size.Step 2:If the EOQ is not feasible,calculate the TC for this price and the smallest quantity for that price.Step 3:Calculate the EOQ for the next lowest price
22、.If it is feasible,stop and calculate the TC for that quantity and price.Step 4:Compare the TC for Steps 2 and 3.Choose the quantity corresponding to the lowest TC.Step 5:If the EOQ in Step 3 is not feasible,repeat Steps 2,3,and 4 until a feasible EOQ is found.27 2007 Pearson EducationAll-Unit Quant
23、ity Discounts:ExampleCost/Unit$3$2.96$2.92Order Quantity5,00010,000Order Quantity5,00010,000Total Material Cost28 2007 Pearson EducationAll-Unit Quantity Discount:ExampleOrder quantityUnit Price0-5000$3.005001-10000$2.96Over 10000$2.92q0=0,q1=5000,q2=10000C0=$3.00,C1=$2.96,C2=$2.92D=120000 units/yea
24、r,S=$100/lot,h=0.229 2007 Pearson EducationAll-Unit Quantity Discount:ExampleStep 1:Calculate Q2*=Sqrt(2DS)/hC2=Sqrt(2)(120000)(100)/(0.2)(2.92)=6410Not feasible(6410 10001)Calculate TC2 using C2=$2.92 and q2=10001TC2=(120000/10001)(100)+(10001/2)(0.2)(2.92)+(120000)(2.92)=$354,520Step 2:Calculate Q
25、1*=Sqrt(2DS)/hC1=Sqrt(2)(120000)(100)/(0.2)(2.96)=6367Feasible(5000636710000)StopTC1=(120000/6367)(100)+(6367/2)(0.2)(2.96)+(120000)(2.96)=$358,969TC2 TC1 The optimal order quantity Q*is q2=1000130 2007 Pearson EducationAll-Unit Quantity DiscountsuSuppose fixed order cost were reduced to$4 Without d
26、iscount,Q*would be reduced to 1265 units With discount,optimal lot size would still be 10001 unitsuWhat is the effect of such a discount schedule?Retailers are encouraged to increase the size of their orders Average inventory(cycle inventory)in the supply chain is increased Average flow time is incr
27、eased Is an all-unit quantity discount an advantage in the supply chain?31 2007 Pearson Education利用数量折扣获取规模经济利用数量折扣获取规模经济u全部单位数量折扣uqiQiqi+1uTCi（R/Qi）S+(Qi/2)+RCi32 2007 Pearson Education月需求量1000订购成本100储存成本20%订购数量单价0-500035001-100002.9610000-2.92Drug online33 2007 Pearson Educationu解：q00，q15000，q2100
28、00uC03，C12.96，C22.92uR=120000,S=100,h0.2uQ0*=(2RS/hC)1/2 (2*120000*100/3*0.2)1/2 6324uq15000时，uTC0=(R/q1)S+(q1/2)hC1+RC1=120000/5000*100+5000/2*0.2*2.96+120000*2.96359080uQ1*=(2RS/hC)1/2 (2*12000*100/2.96*0.2)1/2 6367uQ1*=6367时，uTC1=(R/Q1)S+(Q1/2)hC+RC1=358969uQ2*=(2RS/hC)1/2 (2*12000*100/3*0.2)1/2
29、6410uq2=10000时，uTC2=(R/q2)S+(q1/2)hC+RC1=35452034 2007 Pearson EducationWhy Quantity Discounts?uCoordination in the supply chain Commodity products Products with demand curve 2-part tariffs Volume discounts35 2007 Pearson EducationCoordination forCommodity ProductsuD=120,000 bottles/yearuSR=$100,hR=
30、0.2,CR=$3uSS=$250,hS=0.2,CS=$2Retailers optimal lot size=6,324 bottlesRetailer cost=$3,795;Supplier cost=$6,009Supply chain cost=$9,80436 2007 Pearson EducationCoordination forCommodity ProductsuWhat can the supplier do to decrease supply chain costs?Coordinated lot size:9,165;Retailer cost=$4,059;S
31、upplier cost=$5,106;Supply chain cost=$9,165uEffective pricing schemes All-unit quantity discount$3 for lots below 9,165$2.9978 for lots of 9,165 or more Pass some fixed cost to retailer(enough that he raises order size from 6,324 to 9,165)37 2007 Pearson EducationQuantity Discounts WhenFirm Has Mar
32、ket PoweruNo inventory related costsuDemand curve360,000-60,000pWhat are the optimal prices and profits in the following situations?The two stages coordinate the pricing decision Price=$4,Profit=$240,000,Demand=120,000 The two stages make the pricing decision independently Price=$5,Profit=$180,000,D
33、emand=60,00038 2007 Pearson EducationTwo-Part Tariffs andVolume DiscountsuDesign a two-part tariff that achieves the coordinated solutionuDesign a volume discount scheme that achieves the coordinated solutionuImpact of inventory costs Pass on some fixed costs with above pricing39 2007 Pearson Educat
34、ionLessons from Discounting SchemesuLot size based discounts increase lot size and cycle inventory in the supply chainuLot size based discounts are justified to achieve coordination for commodity productsuVolume based discounts with some fixed cost passed on to retailer are more effective in general
35、 Volume based discounts are better over rolling horizon40 2007 Pearson Educationu为什么采取数量折扣的策略u1）供应链的协调u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。41 2007 Pearson EducationuA、对最终产品数量折扣案例uVitamin co：R10000，S100，h20，Cm3；u计算出Q*6324，TC3795u制造商：S250，C02，h20。u制造商订购成本120000/6324*2504744
36、u制造商年存储成本6324/2*2*0.21265u总成本4744+12656009u供应链总成本6009+37959804u如果Q*9165，则：u供应链总成本120000/9165*100+9165/2*3*0.2+120000/9165*250+9165/2*2*0.2 4059+51069165u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 2007 Pearson Educationu引论：u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。u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
37、运作部门降低固定成本，营销部门提供数量折扣？！（思考）43 2007 Pearson EducationuB、对公司有市场控制权的产品实行数量折扣u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。ur销=（360000-60000p）p-（360000-60000p）c1ur=360000-120000p+60000c1=0uP=5 q=60000 r销=60000 r制=120000 r供=18000u整合后：p=4 q=120000 r供=18000044 2007 Pearson Educationu协调方法：u第一种、两部分定价：u制造商先索
38、取全部利润作为前期特许经营费，再将产品以成本出售u第二种、以总量为基础的数量折扣uQ12000,p=3.5u注意：零售商在期末加大采购，即曲棍球现象。u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）45 2007 Pearson Educationu2）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46 2007 Pearson EducationShort-Term Discounting:Trade PromotionsuTrade promotions are price discounts for a limited period of ti
39、me(also may require specific actions from retailers,such as displays,advertising,etc.)uKey goals for promotions from a manufacturers perspective:Induce retailers to use price discounts,displays,advertising to increase sales Shift inventory from the manufacturer to the retailer and customer Defend a
40、brand against competition Goals are not always achieved by a trade promotionuWhat is the impact on the behavior of the retailer and on the performance of the supply chain?uRetailer has two primary options in response to a promotion:Pass through some or all of the promotion to customers to spur sales
41、 Purchase in greater quantity during promotion period to take advantage of temporary price reduction,but pass through very little of savings to customers47 2007 Pearson EducationShort Term DiscountingQ*:Normal order quantityC:Normal unit costd:Short term discountD:Annual demandh:Cost of holding$1 pe
42、r yearQd:Short term order quantitydCChdCdDQQd-+)-(=*Forward buy=Qd-Q*48 2007 Pearson EducationShort Term Discounts:Forward BuyingNormal order size,Q*=6,324 bottles Normal cost,C=$3 per bottleDiscount per tube,d=$0.15Annual demand,D=120,000Holding cost,h=0.2Qd=Forward buy=49 2007 Pearson EducationPro
43、motion Pass Throughto ConsumersDemand curve at retailer:300,000-60,000pNormal supplier price,CR=$3.00 Optimal retail price=$4.00 Customer demand=60,000Promotion discount=$0.15 Optimal retail price=$3.925 Customer demand=64,500Retailer only passes through half the promotion discount and demand increa
44、ses by only 7.5%50 2007 Pearson EducationTrade PromotionsuWhen a manufacturer offers a promotion,the goal for the manufacturer is to take actions(countermeasures)to discourage forward buying in the supply chainuCounter measures EDLP Scan based promotions Customer coupons51 2007 Pearson Education短期折扣
45、：商业促销短期折扣：商业促销u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u经销商选择：u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 2007 Pearson Educationu折扣价格下的最优订购数量：u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。uQddR/（C-d）h+CQ*/(C-d)u超前采购量 Qd-Q*u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 2007 Pearson Education案例：案例：DODO公司公司R=120000,C
46、M=3,hR=120000,CM=3,h0.20.2，Q Q*=6324,d=6324,d0.150.15，求零售商订，求零售商订购数量？购数量？uQddR/（C-d）h+CQ*/(C-d)u0.15*120000/（3-0.15）0.2+3*6324/（3-0.15）38236u循环库存19118u平均周转时间38236/2*120000u0.16年1.9118月u超前采购量38236-632431912uDO公司在今后3个月将不采购！导致零售商库存大增。只有当制造商无意建立了大量剩余库存，或者想使低谷期需求量增加，才会支持超前采购。实际上，制造商经常根据预测的计划促销活动建立库存。54 2
47、007 Pearson Education总结：总结：u1、商业促销通常会增加循环库存，损害供应链利益，许多公司，如walm，P&G采用low price every day，而不提供短期折扣。u2、商业促销作为竞争性反应是有用的，如peps，&cocalu3、管理者应当精心设计促销，限制超前采购，并刺激更多的向顾客价值让度u4、充分运用现代信息技术，以零售扫描数据为基础实施折扣；或者按以往销售业绩，分配折扣商品数量。55 2007 Pearson EducationEstimating Cycle Inventory-Related Costs in PracticeuInventory h
48、olding cost Cost of capital Obsolescence cost Handling cost Occupancy cost Miscellaneous costsuOrder cost Buyer time Transportation costs Receiving costs Other costs56 2007 Pearson EducationLevers to Reduce Lot Sizes Without Hurting CostsuCycle Inventory Reduction Reduce transfer and production lot
49、sizes Aggregate fixed costs across multiple products,supply points,or delivery points Are quantity discounts consistent with manufacturing and logistics operations?Volume discounts on rolling horizon Two-part tariff Are trade promotions essential?EDLP Based on sell-thru rather than sell-in57 2007 Pe
50、arson Education在实践中估测与循环库存相关的费用在实践中估测与循环库存相关的费用u1、库存存储成本u资本成本：股本成本、债务成本和税收抵免u报废成本：质量退化和过时u管理成本：接收和储存管理成本（阶梯性）u空间占用成本（阶梯性）u2、订购成本u采购员时间u运输费用u接收成本u其他成本58 2007 Pearson EducationSummary of Learning ObjectivesuHow are the appropriate costs balanced to choose the optimal amount of cycle inventory in the s
