供應鏈物流管理中科院 龔其國三chapter7-8

1、Planning and Managing Inventories ina Supply ChainOptimal Matching of Supply and Demand10/1/2018S. Chopra/Inventory1OutlineThe role of inventory in the supply chainWhy hold inventory?Economies of scaleBatch size and cycle time Quantity discountsShort term discounts / Trade promotionsStochastic varia

2、bility of supply and demand Evaluating service level given safety inventory Evaluating safety inventory given desired service levelLevers to improve performance10/1/2018S. Chopra/Inventory2Role of Inventory in the Supply ChainOverstocking: Amount available exceeds demand Liquidation, Obsolescence, H

3、oldingUnderstocking: Demand exceeds amount available Lost margin and future salesGoal: Matching supply and demand10/1/2018S. Chopra/Inventory3Role of Inventory in the Supply Chain10/1/2018S. Chopra/Inventory4Seasonal InventorySafety InventoryCycle InventoryEconomies of ScaleSeasonal VariabilitySuppl

4、y / Demand VariabilityReduce Buffer InventoryReduce Waiting TimeReduce Material Flow TimeImproved ForecastingImprove Matching of Supply and DemandWhy hold cycle inventory?Economies of scaleFixed costs associated with lots Quantity discountsTrade Promotions10/1/2018S. Chopra/Inventory5Fixed costs: Op

5、timal Lot Size and ReorderInterval (EOQ)R:Annual demandS: Setup or Order Cost C:Cost per unith: Holding cost per year as a fraction of product costH:Holding cost per unit per yearQ:Lot SizeT: Reorder interval10/1/2018S. Chopra/Inventory6H = hCQ =2RS HT =2S RHExampleDemand, R = 12,000 computers per y

6、ear Unit cost, C = $500Holding cost, h = 0.2Fixed cost, S = $4,000/orderQ = 980 computersCycle inventory =Q/2 = 490Flow time = Q/2R = 0.49 monthReorder interval, T = 0.98 month10/1/2018S. Chopra/Inventory7Key Points from BatchingIn deciding the optimal lot size the trade off is between setup (order)

7、 cost and holding cost.If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. Cycle inventory (in days of demand) should decrease as demand increases.If lot size is to be reduced, one has to reduce fixed order cost. To reduce l

8、ot size by a factor of 2, order cost has to be reduced by a factor of 4.10/1/2018S. Chopra/Inventory8Strategies for reducing fixed costsWal-Mart: 3 day replenishment cycleSeven Eleven Japan: Multiple daily replenishment P&G: Mixed truck loadsEfforts required in:Transportation (Cross docking) Informa

9、tionReceivingAggregate across products, supply points, or delivery points.10/1/2018S. Chopra/Inventory9Lot Sizing with Multiple ProductsDemand per yearRL = 12,000; RM = 1,200; RH = 120Common transportation cost, S = $4,000Product specific order costsL = $1,000; sM = $1,000; sH = $1,000Holding cost,

10、h = 0.2Unit costCL = $1,000; CM = $1,000; CH= $1,00010/1/2018S. Chopra/Inventory10Delivery OptionsNo Aggregation: Each product ordered separatelyComplete Aggregation: All products delivered on each truckTailored Aggregation: Selected subsets ofproductss on each truck10/1/2018S. Chopra/Inventory11No

11、Aggregation: Order each productindependentlyTotal cost = $155,14010/1/2018S. Chopra/Inventory12LiteproMedproHeavyproDemand peryear12,0001,200120Fixed cost /order$5,000$5,000$5,000Optimalorder size1,095346110Orderfrequency11.0 / year3.5 / year1.1 / yearAnnual cost$109,544$34,642$0,954Complete Aggrega

12、tion: Order allproducts jointlyAnnual order cost = 9.75$7,000 = $68,250Annual total cost = $136,52810/1/2018S. Chopra/Inventory13LiteproMedproHeavyproDemand peryear12,0001,200120Orderfrequency9.75/year9.75/year9.75/yearOptimal order size1,23012312.3Annual holding cost$61,512$6,151$615Tailored Aggreg

13、ation: OrderingSelected SubsetsStep 1: Identify most frequently ordered productStep 2: Identify frequency of other products as a multipleStep 3: Recalculate ordering frequency of most frequently ordered productStep 4: Identify ordering frequency of all products10/1/2018S. Chopra/Inventory14Tailored

14、Aggregation: Order selectedsubsetsAnnual order cost = $61,560 Total annual cost = $131,00410/1/2018S. Chopra/Inventory15LiteproMedproHeavyproDemand peryear12,0001,200120Orderfrequency10.8/year5.4/year2.16/yearOptimal order size1,11122256Annual holding cost$55,556$11,111$2,778Impact of product specif

15、ic order cost10/1/2018S. Chopra/Inventory16Product specific order cost = $1000Product specific order cost = $3000No Aggregation$155,140$183,564Complete Aggregation$136,528$186,097Tailored Aggregation$131,004$165,233Lessons From AggregationAggregation allows firm to lower lot size without increasing

16、costComplete aggregation is effective if product specific fixed cost is a small fraction of joint fixed costTailored aggregation is effective if product specific fixed cost is large fraction of joint fixed cost10/1/2018S. Chopra/Inventory17Quantity DiscountsLot size based All units Marginal unitVolu

17、me basedHow should buyer react?What are appropriate discounting schemes?10/1/2018S. Chopra/Inventory18All-Unit Quantity DiscountsCost/UnitTotal Material Cost$3$2.96$2.925,00010,0005,00010,000Order QuantityOrder Quantity10/1/2018S. Chopra/Inventory19All-Unit Quantity DiscountsEvaluate EOQ for price i

18、n range qi to qi+1 If qi EOQ qi+1 , evaluate cost of ordering EOQ If EOQ qi, evaluate cost of ordering qi If EOQ qi+1 , evaluate cost of ordering qi+1Evaluate minimum cost over all price ranges10/1/2018S. Chopra/Inventory20Marginal Unit Quantity DiscountsCost/UnitTotal Material Cost$3$2.96$2.925,000

19、10,0005,00010,000Order QuantityOrder Quantity10/1/2018S. Chopra/Inventory21Marginal-Unit Quantity DiscountsEvaluate EOQ for price in range qi to qi+12R(S + V i - qi Ci)EOQ =hCi If qi EOQ qi+1 , evaluate cost of ordering EOQ If EOQ qi, evaluate cost of ordering qi If EOQ qi+1 , evaluate cost of order

20、ingEvaluate minimum cost over all price ranges10/1/2018S. Chopra/Inventory22Why Quantity Discounts?Coordination in the supply chainCommodity productsProducts with demand curve2-part tariffsVolume discounts10/1/2018S. Chopra/Inventory23Coordination for CommodityProductsR = 120,000 bottles/yearSR = $1

21、00, hR = 0.2, CR = $3SS = $250, hS = 0.2, CS = $2Retailers optimal lot size = 6,324 bottlesRetailer cost = $3,795; Supplier cost = $6,009 Supply chain cost = $9,80410/1/2018S. Chopra/Inventory24Coordination for CommodityProductsWhat can the supplier do to decrease supply chain costs?Coordinated lot

22、size: 9,165; Retailer cost = $4,059; Supplier cost = $5,106; Supply chain cost = $9,165.Effective pricing schemesAll unit quantity discount $3 for lots below 9,165 $2.9978 for lots of 9,165 or morePass some fixed cost to retailer (enough that he raises order size from 6,324 to 9,165)10/1/2018S. Chop

23、ra/Inventory25Quantity Discounts When Firm hasMarket PowerNo inventory related costs Demand 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 = 120,000The two stages make the

24、pricing decision independently Price = $5, Profit = $180,000, Demand = 60,00010/1/2018S. Chopra/Inventory26Two Part Tariffs and VolumeDiscountsDesign a two-part tariff that achieves the coordinated solution.Design a volume discount scheme that achieves the coordinated solution.Impact of inventory co

25、stsPass on some fixed costs with above pricing10/1/2018S. Chopra/Inventory27Lessons From Discounting SchemesLot size based discounts increase lot size and cycle inventory in the supply chainLot size based discounts are justified to achieve coordination for commodity productsVolume based discounts wi

26、th some fixed cost passed on to retailer are more effective in generalVolume based discounts are better over rolling horizon10/1/2018S. Chopra/Inventory28Short Term DiscountingQ*: Normal order quantityC: Normal unit costd: Short term discountR: Annual demandh: Cost of holding $1 per yearQd: Short te

27、rm order quantityForward buy = Qd - Q*CQ*dRQd=+(C - d )hC - d10/1/2018S. Chopra/Inventory29Short Term Discounts: ForwardbuyingNormal order size, Q* = 6,324 bottles Normal cost, C = $3 per bottle Discount per tube, d = $0.15Annual demand, R = 120,000Holding cost, h = 0.2Qd =Forward buy =10/1/2018S. C

28、hopra/Inventory30Promotion pass through to consumersDemand curve at retailer: 300,000 - 60,000p Normal 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 th

29、e promotion discount and demand increases by only 7.5%10/1/2018S. Chopra/Inventory31Weekly Consumption of ChickenNoodle Soup35030025020015010050010/1/2018S. Chopra/Inventory32ConsumptionWeekly Shipments of Chicken NoodleSoup8007006005004003002001000ShipmentsConsumption10/1/2018S. Chopra/Inventory33T

30、rade PromotionsGoal is to discourage forward buying in the supply chainCounter measuresEDLPScan based promotions Customer coupons10/1/2018S. Chopra/Inventory34Levers to Reduce Lot Sizes WithoutHurting CostsCycle Inventory ReductionReduce transfer and production lot sizes Aggregate fixed cost across

31、multiple products, supply points, or delivery pointsAre quantity discounts consistent with manufacturing and logistics operations? Volume discounts on rolling horizon Two-part tariffAre trade promotions essential?EDLPBase on sell-thru rather than sell-in10/1/2018S. Chopra/Inventory35Why hold Safety

32、Inventory?Demand uncertaintySupply uncertaintyMeasures of product availabilityProduct fill rate (fr) Order fill rateCycle service level (CSL)10/1/2018S. Chopra/Inventory36Replenishment policiesWhen to reorder?How much to reorder?Continuous Review: Order fixed quantity when total inventory drops belo

33、w Reorder Point (ROP)Periodic Review: Order at fixed time intervals to raise total inventory to Order up to Level (OUL)10/1/2018S. Chopra/Inventory37Continuous Review Policy: SafetyInventory and Cycle Service LevelL: Lead time for replenishmentR: Average demand per unit timesR:Standard deviation of

34、demand per periodRL: Mean demand during lead timesL: Standard deviation of demand during lead timeCSL: Cycle service levelss: Safety inventoryROP: Reorder pointAverage Inventory = Q/2 + ss10/1/2018S. Chopra/Inventory38RL = RLs L =L s Rss = F -1 (CSL) sSLROP = RL + ssCSL = F (ROP, RL ,s L)Example 8.1

35、 (Continuous ReviewPolicy)R = 2,500 /week; sR = 500L = 2 weeks; Q = 10,000; ROP = 6,000s L = s RL =ss = ROP - RL =Average Inventory=Average Flow Time =Cycle service level, CSL = F(RL+ ss, RL, sL) =10/1/2018S. Chopra/Inventory39Example 8.2: Evaluating SafetyInventory Given CSLR = 2,500/week; sR = 500

36、L = 2 weeks; Q = 10,000; CSL = 0.90ss = FS-1(CSL)sL = ROP =Factors driving safety inventoryReplenishment lead timedemand uncertainty10/1/2018S. Chopra/Inventory40Fill RateProportion of customer demand satisfied from stockESC is the expected shortage per cycless is the safety inventoryQ is the order

37、quantityESC = -ss1-NORMDIST(ss/sL, 0, 1, 1) + sL NORMDIST(ss/ sL, 0, 1, 0)10/1/2018S. Chopra/Inventory41fr = 1- ESCQESC = -ss1- F ss S sL + sf ss LS sL Example 8.2: Evaluating Fill Ratess = 1,000, Q = 10,000, Fill Rate (fr) = ?ESC = -ss1-NORMDIST(ss/sL, 0, 1, 1) +sL NORMDIST(ss/sL, 0, 1, 0)= -1,0001

38、-NORMDIST(1,000/707, 0, 1, 1) +707 NORMDIST(1,000/707, 0, 1, 0)= 25.13fr = (Q - ESC)/Q = (10,000 - 25.13)/10,000 = 0.9975.10/1/2018S. Chopra/Inventory42Evaluating Safety Inventory GivenDesired Fill RateIf desired fill rate is fr = 0.975, how much safety inventory should be held?ESC = (1 - fr)Q = 250

39、Solvess ss + ESC =250 = -ss 1 -fFSLSL L ss ss250 = -ss1 - NORMSDISTNORMDIST ,1,1,0+LL L10/1/2018S. Chopra/Inventory43Evaluating Safety Inventory Given FillRate10/1/2018S. Chopra/Inventory44Fill RateSafety Inventory97.5%6798.0%18398.5%32199.0%49999.5%767Factors Affecting Fill RateSafety inventory: Fi

40、ll rate increases if safety inventory is increased. This also increases the cycle service level.Lot size: Fill rate increases on increasing thelot size even change.though cycle service level does not10/1/2018S. Chopra/Inventory45Periodic Review Policy: Safety InventoryL: Lead timeT: Reorder interval

41、R: Average demand per unit timesR: Standard deviation ofdemand per unit timesL+T: Standard deviation of demand during L+T periodsCSL: Cycle service level ss: Safety inventory OUL: Order up to level10/1/2018S. Chopra/Inventory46RT + L = (T + L)Rs T + L = s RL + T ss = F -1 (CSL) sST + LOUL = RT + L +

42、 ssExample: Periodic Review PolicyR = 2,500/week; sR = 500L = 2 weeks; T = 4 weeks; CSL = 0.90What is the required safety inventory?Factors driving safety inventoryDemand uncertainty Replenishment lead timeReorder interval10/1/2018S. Chopra/Inventory47Impact of Supply UncertaintyR: Average demand pe

43、r periodsR: Standard deviation of demand per periodL: Average lead timesL: Standard deviation of lead timeRL= RLs L=+ R2 s2Ls 2RL10/1/2018S. Chopra/Inventory48Impact of Supply UncertaintyR = 2,500/day; sR = 500L = 7 days; Q = 10,000; CSL = 0.90Safety inventory when sL= 0 is 1,695Safety inventory whe

44、n sL = 1 is 3,625 Safety inventory when sL = 2 is 6,628 Safety inventory when sL = 3 is 9,760 Safety inventory when sL = 4 is 12,927 Safety inventory when sL = 5 is 16,109Safety inventory when sL = 6 is 19,29810/1/2018S. Chopra/Inventory49Basic Quick Response InitiativesReduce information uncertaint

45、y in demand Reduce replenishment lead timeReduce supply uncertainty or replenishment lead time uncertaintyIncrease reorder frequency or go to continuous review10/1/2018S. Chopra/Inventory50Accurate Response: The Impact ofInventory PoolingWhich of the two systems provides a higher level of service fo

46、r a given level of safety stock?System A (Decentralized)System B (Centralized)(Ri ,s i)(RC ,s C)Rkk=s 2 + 2 cov(i, j)RCi=1s CR ;iRii=1i j10/1/2018S. Chopra/Inventory51Factors Affecting Value of AggregationDemand CorrelationCoefficient of Variation of demand Value of product10/1/2018S. Chopra/Invento

47、ry52Impact of Correlation on Benefit FromAggregation0.60.50.40.30.20.1000.20.40.60.8110/1/2018S. Chopra/Inventory53BenefitImpact of cv and Product Value onBenefit From Aggregation10/1/2018S. Chopra/Inventory54MotorsCleanerMean demand201,000SD of demand40100Disaggregate cv20.1Value/Unit$500$30Disaggr

48、egate ss$105,600,000$15,792,000Aggregate cv0.050.0025Aggregate ss$2,632,000$394,770Holding Cost Saving$25,742,000$3,849,308Saving / Unit$7.74$0.046Methods of Accurate ResponsePhysical Centralization Information centralization SpecializationProduct substitutionRaw material commonality (postponement)1

49、0/1/2018S. Chopra/Inventory55Example 8.9: Value of ComponentCommonality45000040000035000030000025000020000015000010000050000012345678910/1/2018S. Chopra/Inventory56SSMass Customization I: CustomizeServices Around Standardized ProductsSource: B. Joseph PineERYDeliver customized services as well as st

50、andardized products and servicesMarket customized services with standardized products or servicesContinue producing standardized products or servicesContinue developing standardized products or services10/1/2018S. Chopra/Inventory57DEVELOPMENTPRODUCTIONMARKETINGDELIVMass Customization II: CreateCustomizable Products and ServicesERYDeliver standard (but customizable) products or servicesMarket customizable products or servicesProduce standard (but customizable) products or servicesDevelop customizable products or servicesS. Chopra/I