1、Determining Optimal Level ofAvailability in a Supply Chain9/30/2018S. Chopra/Availability1OutlineDetermining optimal level of product availability Single order in a season Continuously stocked itemsOrdering under capacity constraintsLevers to improve supply chain profitability Contracts9/30/2018S. C

2、hopra/Availability2Mattel, Inc. & Toys “R” UsMattel was hurt last year by inventory cutbacks at Toys “R” Us, and officials are also eager to avoid a repeat of the 1998 Thanksgiving weekend. Mattel had expected to ship a lot of merchandise after the weekend, but retailers, wary of excess inventory, s

3、topped ordering from Mattel. That led the company to report a $500 million sales shortfall in the last weeks of the year. For the crucial holiday selling season this year, Mattel said it will require retailers to place their full orders before Thanksgiving. And, for the first time, the company will

4、no longer take reorders in December, Ms. Barad said. This will enable Mattel to tailor production more closely to demand and avoid building inventory for orders that dont come.- Wall Street Journal, Feb. 18, 19999/30/2018S. Chopra/Availability3Key QuestionsHow much should Toys R Us order given deman

5、d uncertainty?How much should Mattel order?Will Mattels action help or hurt profitability?What actions can improve supply chain profitability?9/30/2018S. Chopra/Availability4How much to order? Parkas at L.L.Bean9/30/2018S. Chopra/Availability5DemandProbababilityCumulative Probability of demand being

6、 this size or lessProbability of demand greater than this size4.01.01.995.02.03.976.04.07.937.08.15.858.09.24.769.11.35.6510.16.51.4911.20.71.2912.11.82.1813.10.92.0814.04.96.0415.02.98.0216.01.99.0117.011.00.00Parkas at L.L. BeanCost per parka = $45Sale price per parka = $100 Discount price per par

7、ka = $50Holding and transportation cost = $10Profit from selling parka = $100-$45 = $55Cost of overstocking = $45+$10-$50 = $59/30/2018S. Chopra/Availability6Parkas at L.L. BeanExpected demand = 10 (00) parkasExpected profit from ordering 10 (00) parkas= $4999/30/2018S. Chopra/Availability7Parkas at

8、 L.L. Bean9/30/2018S. Chopra/Availability8Additional 100sExpected Marginal BenefitExpected Marginal CostExpected Marginal Contribution11th5500.49 = 2695500.51 = 2552695-255 = 244012th5500.29 = 1595500.71 = 3551595-355 = 124013th5500.18 = 990500.82 = 410990-410 = 58014th5500.08 = 440500.92 = 460440-4

9、60 = -2015th5500.04 = 220500.96 = 480220-480 = -26016th5500.02 = 110500.98 = 490110-490 = -38017th5500.01 = 55500.99 = 49555-495 = -440Optimal level of servicer = sale price; s = outlet or salvage price;c = purchase priceCSL = Probability that demand will be at or below reorder pointAt optimal order

10、 size,Expected Marginal Benefit from raising order size = (1-CSL*)(r - c) = Expected Marginal Cost= CSL*(c - s).(1-CSL*)Cu= CSL* Co,CSL* = Cu / (Cu + Co)9/30/2018S. Chopra/Availability9Order Quantity for a Single OrderCo= Cost of overstocking= $5= Profit from sale=Cost of understocking= $55= Optimal

11、 order sizeCSL =Pr ob(Demand R*) Cu55Cu= 0.917Cu + Co55 + 5R*9/30/2018S. Chopra/Availability10Optimal Order Quantity1.20.91710.80.60.40.20Optimal Order Quantity = 139/30/2018S. Chopra/Availability11ProbabilityHow to Estimate DemandDistribution?Historical data: Time series forecastingDependent factor

12、s: Regression, causal forecastingExpert opinion: Buying committeeKey: Forecast must include estimated demand and uncertainty (standard deviation) of demand9/30/2018S. Chopra/Availability12Continuously Stocked Items: OptimalSafety Inventory LevelsFor each order cycle Benefit of increasing safety stoc

13、k by one unit= (1-CSL)Cu Cost of increasing safety stock by one unit = HQ*/RwhereCSL = probability of not stocking out in a cycle with current level of safety stock = Cycle Service LevelH = cost of holding one unit for one year R = Annual demandQ* = Economic order quantity9/30/2018S. Chopra/Availabi

14、lity13Optimal Safety Inventory LevelsCSL = 1-HQ*/CuRR = 100 gallons/week; sR= 20; H = $0.6/gal./year L = 2 weeks; Q = 400; ROP = 300.What is the imputed cost of stocking out?9/30/2018S. Chopra/Availability14Ordering Under Capacity ConstraintsAvailable Capacity = 1,500.9/30/2018S. Chopra/Availability

15、15AutumnLeavesRuffleRetail price$150$200$250Purchase price$75$90$110Salvage price$40$50$90Mean Demand1000500250Standard deviation of demand250175125Assuming No Capacity Constraints9/30/2018S. Chopra/Availability16AutumnLeavesRuffleri-ci$150-$75=$75$200-$90=$110$250-$110=$140ri-si$150-$40=$110$200 -$

16、50 =$150$250-$90= $160Critical Fractile75/110 =0.68110/150= 0.73140/160=0.875zi0.470.611.15Q *i1118607394Ordering Under Capacity ConstraintsStep 0: Set Qi = 0 for all products i.Step 1: Compute the marginal contribution for all products i.Step 2: Increase Qj, for the product j with the largest margi

17、nal contribution, by 1.Step 3: If all the capacity is not used up and there is some product with a positive marginal contribution, return to Step 1, else stop.9/30/2018S. Chopra/Availability17Marginal Contribution Calculations9/30/2018S. Chopra/Availability18Order QuantityMarginal ContributionCapaci

18、ty leftAutumnLeavesRuffleAutumnLeavesRuffle150000074.997109.679136.3601490001074.997109.679135.61113600014074.997109.679109.69113500015074.997109.679106.103134001015074.997109.617106.103133002015074.997109.543106.103132003015074.997109.457106.103131004015074.997109.357106.103890038023074.99773.03370

19、.1708801038023074.99673.03370.1708702038023074.99573.03370.17029058040023069.88767.42270.17028058040024069.88767.42265.101178844626553.19653.17652.359078944626553.07353.17652.359Ordering Under Capacity ConstraintsAssume N products for i = 1, ., N, all produced using the same capacityTotal available

20、capacity = Bri = sale price; si = outlet or salvage price; ci = purchase price. All are for product iMarginal contribution of raising order size of product i from Qi to Qi + 1 = (1-pi)(ri - ci) - pi(ri - si) where pi is the probability that demand for product i will be Qi or less.9/30/2018S. Chopra/

21、Availability19Levers for Increasing Supply ChainProfitabilityIncrease salvage value or decrease margin lost from stockoutImproved forecasting to lower uncertaintyQuick response to increase number of orders per seasonPostponement of product differentiation Tailored sourcing9/30/2018S. Chopra/Availabi

22、lity20Impact of Improving ForecastsDemand: Normally distributed with a mean of R= 350 and standard deviation of sR = 100 Purchase price = $100Retail price = $250 Disposal value = $85Holding cost for season = $5How many units should be ordered as sR changes?9/30/2018S. Chopra/Availability21Impact of

23、Improving Forecasts9/30/2018S. Chopra/Availability22sRO*Expected OverstockExpected UnderstockExpected Profit150526186.78.6$47,469120491149.36.9$48,47690456112.05.2$49,4826042074.73.5$50,4883038537.31.7$51,494035000$52,500Quick Response: Multiple Orders perSeasonOrdering shawls at a department storeS

24、elling season = 14 weeks Cost per handbag = $40 Sale price = $150 Disposal price = $30Holding cost = $2 per weekExpected weekly demand = 20SD of weekly demand = 159/30/2018S. Chopra/Availability23Impact of Quick Response9/30/2018S. Chopra/Availability24Single OrderTwo Orders in SeasonService LevelOr

25、der SizeEnding Invent.Expect. ProfitInitial OrderOULfor 2nd OrderAverage Total OrderEnding Invent.Expect. Profit0.9637897$23,62420920934969$26,5900.9436786$24,03420120134260$27,0850.9135573$24,61719319333252$27,1540.8734366$24,38618418431943$26,9440.8132955$24,60917417431336$27,4130.7531741$25,20516

26、616630232$26,916Forecast Improves for Second Order(SD=3 instead of 15)9/30/2018S. Chopra/Availability25Single OrderTwo Orders in SeasonService LevelOrder SizeEnding Invent.Expect. ProfitInitial OrderOULfor 2nd OrderAverage Total OrderEnding Invent.Expect. Profit0.9637896$23,70720915329219$27,0070.94

27、36784$24,30320115229318$27,3710.9135576$24,15419315028817$26,9460.8734363$24,80718414828814$27,5830.8132952$24,99817414628314$27,1620.7531744$24,88716614528214$27,268Value of Postponement: BenettonFor each colorMean demand = 1,000; SD = 500For each garmentSale price = $50 Salvage value = $10Producti

28、on cost using option 1 (long lead time) = $20Production cost using option 1 (greige thread) = $22What is the value of postponement?Expected profit increases from $94,576 to $98,0929/30/2018S. Chopra/Availability26Value of Postponement with DominantProductColor with dominant demand: Mean = 3,100, SD=

29、 800Other three colors: Mean = 300, SD = 200Expected profit without postponement = $102,205Expected profit with postponement = $99,8729/30/2018S. Chopra/Availability27Tailored Postponement: BenettonProduce Q1 units for each color using Option 1 and QA units (aggregate) using Option 2 Results:Q1 = 80

30、0QA = 1,550Profit = $104,6039/30/2018S. Chopra/Availability28Tailored SourcingSourcing alternatives Low cost, long lead time supplier Cost = $245, Lead time = 9 weeks High cost, short lead time supplier Cost = $250, Lead time = 1 week9/30/2018S. Chopra/Availability29Tailored Sourcing Strategies9/30/

31、2018S. Chopra/Availability30Fraction of demand fromoverseas supplierAnnual Profit0%$37,25050%$51,61360%$53,027100%$48,875Tailored Sourcing: Multiple SourcingSites9/30/2018S. Chopra/Availability31CharacteristicPrimary SiteSecondary SiteManufacturingCostHighLowFlexibility(Volume/Mix)HighLowResponsiven

32、essHighLowEngineeringSupportHighLowDual Sourcing Strategies9/30/2018S. Chopra/Availability32StrategyPrimary SiteSecondary SiteVolume baseddual sourcingFluctuationStable demandProduct baseddual sourcingUnpredictableproducts, Small batchPredictable,large batch productsModel baseddual sourcingNewerprod

33、uctsOlder stableproductsImpact of Supply Chain Contracts onProfitability: Buyback ContractsBuybacks by publishersTech Fiber produces jacket at v = $10 and charges a wholesale price of c = $100. Ski Adventure sells jacket for p = $200. Unsold jackets have no salvage value. Should TF be willing to buy

34、 back unsold jackets? Why?9/30/2018S. Chopra/Availability33BuybackBuyback Contracts9/30/2018S. Chopra/Availability34Wholesale Price cBuy Back Price bOptimal Order size for SAExpected Profit for SAExpected Returns to TFExpected Profit for TFExpected Supply Chain Profit$100$01,000$76,063120$90,000$166

35、,063$100$301,067$80,154156$91,338$171,492$100$601,170$85,724223$91,886$177,610$100$951,501$96,875506$86,935$183,810$110$781,191$78,074239$100,480$178,555$110$1051,486$86,938493$96,872$183,810$120$961,221$70,508261$109,225$179,733$120$1161,501$77,500506$106,310$183,810Quantity Flexibility ContractsIf a retailer order O units the ma