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1、Copyrighted by Pearson1Chapter 12Managing Uncertainty in a Supply Chain: Safety InventoryReading AssignmentChapter 12 (Chopra)Copyrighted by Pearson2Learning Objectives1. Understand the role of safety inventory in a supply chain2. Identify factors that influence the required level of safety inventor

2、y3. Describe different measures of product availability4. Utilize managerial levers available to lower safety inventory and improve product availabilityCopyrighted by Pearson3The Role of Safety Inventory Safety inventory is carried to satisfy demand that exceeds the amount forecasted Raising the lev

3、el of safety inventory increases product availability and thus the margin captured from customer purchases Raising the level of safety inventory increases inventory holding costsCopyrighted by Pearson4The Role of Safety Inventory Three key questions1. What is the appropriate level of product availab

4、ility?2. How much safety inventory is needed for the desired level of product availability?3. What actions can be taken to improve product availability while reducing safety inventory?Copyrighted by Pearson5The Role of Safety InventoryFigure 12-1Copyrighted by Pearson6Determining the Appropriate Lev

5、el Determined by two factors The uncertainty of both demand and supply The desired level of product availability Measuring Demand UncertaintyD = Average demand per period sD =Standard deviation of demand (forecast error) per periodLead time (L) is the gap between when an order is placed and when it

6、is receivedCopyrighted by Pearson7Evaluating Demand Distribution Over L PeriodsDL=Di sL=si2+2rijsisjiji=1Li=1LLDLDDLLss= The coefficient of variationcv=s/mCopyrighted by Pearson8Measuring Product Availability1. Product fill rate (fr) Fraction of product demand satisfied from product in inventory2. O

7、rder fill rate Fraction of orders filled from available inventory3. Cycle service level (CSL) Fraction of replenishment cycles that end with all customer demand being metCopyrighted by Pearson9Replenishment Policies1. Continuous review Inventory is continuously tracked Order for a lot size Q is plac

8、ed when the inventory declines to the reorder point (ROP)2. Periodic review Inventory status is checked at regular periodic intervals Order is placed to raise the inventory level to a specified thresholdCopyrighted by Pearson10Evaluating Cycle Service Level and Fill Rate Evaluating Safety Inventory

9、Given a Replenishment PolicyExpected demand during lead time = DLSafety inventory, ss = ROP DLCopyrighted by Pearson11Evaluating Cycle Service Level and Fill RateAverage demand per week, D = 2,500 Standard deviation of weekly demand, sD = 500 Average lead time for replenishment, L = 2 weeks Reorder

10、point, ROP = 6,000 Average lot size, Q = 10,000Safety inventory, ss = ROP DL = 6,000 5,000 = 1,000Cycle inventory = Q/2 = 10,0002 = 5,000Copyrighted by Pearson12Evaluating Cycle Service Level and Fill RateAverage inventory = cycle inventory + safety inventory = 5,000 + 1,000 = 6,000Average flow time

11、 = average inventory/throughput= 6,000/2,500 = 2.4 weeksCopyrighted by Pearson13Evaluating Cycle Service Level and Fill Rate Evaluating Cycle Service Level Given a Replenishment PolicyCSL = Prob(ddlt of L weeks ROP)CSL = F(ROP, DL, sL) = NORMDIST(ROP, DL, sL, 1)(ddlt = demand during lead time)Copyri

12、ghted by Pearson14Evaluating Cycle Service Level and Fill RateQ = 10,000, ROP = 6,000, L = 2 weeks D = 2,500/week, sD = 500DL=DL= 22,500sL=LsD=2 500 = 707CSL = F(ROP,DL,sL) = NORMDIST(ROP,DL,sL,1)= NORMDIST(6,000,5,000,707,1) = 0.92Copyrighted by Pearson15Evaluating Fill Rate Given a Replenishment P

13、olicy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per replenishment cycle Product fill ratefr = 1 ESC/Q = (Q ESC)/QCopyrighted by Pearson16Evaluating Fill Rate Given a Replenishment PolicyESC=(xROP)f(x)dxx=ROPESC= ss1F

14、ssssL+sLfssssLESC= ss1NORMDIST(ss/sL,0,1,1)+sLNORMDIST(ss/sL,0,1,0)Copyrighted by Pearson17Evaluating Fill Rate Given a Replenishment PolicyLot size, Q = 10,000 Average demand during lead time, DL = 5,000 Standard deviation of demand during lead time, sL = 707Safety inventory, ss = ROP DL = 6,000 5,

15、000 = 1,000ESC= 1,0001NORMDIST(1,000/ 707,0,1,1)+707NORMDIST(1,000/ 707,0,1,0) = 25fr = (Q ESC)/Q = 110,000 252/10,000 = 0.9975Copyrighted by Pearson18Evaluating Fill Rate Given a Replenishment PolicyFigure 12-2Copyrighted by Pearson19Evaluating Safety Inventory Given Desired Cycle Service LevelDesi

16、red cycle service level = CSL Mean demand during lead time = DL Standard deviation of demand during lead time = LProbability(demand during lead time DL + ss) = CSLIdentify safety inventory so thatF(DL + ss, DL, sL) = CSLCopyrighted by Pearson20Evaluating Safety Inventory Given Desired Cycle Service

17、LevelDL+ss=F1(CSL,DL,sL) =NORMINV(CSL,DL,sL)ss=F1(CSL,DL,sL) DL=NORMINV(CSL,DL,sL) DLorss=FS1(CSL)sL=FS1(CSL)LsD=NORMSINV(CSL)LsDCopyrighted by Pearson21Evaluating Safety Inventory Given Desired Cycle Service LevelQ = 10,000, CSL = 0.9, L = 2 weeks D = 2,500/week, sD = 500DL=DL= 22,500 = 5,000sL=LsD

18、=2 500 = 707ss=Fs1(CSL)sL=NORMSINV(CSL)sL=NORMSINV(0.90)707 = 906Copyrighted by Pearson22Evaluating Safety Inventory Given Desired Fill Rate Expected shortage per replenishment cycle isESC = (1 fr)Q No equation for ss Try values or use GOALSEEK in ExcelCopyrighted by Pearson23Evaluating Safety Inven

19、tory Given Desired Fill RateDesired fill rate, fr = 0.975 Lot size, Q = 10,000 boxes Standard deviation of ddlt, sL = 707ESC = (1 fr)Q = (1 0.975)10,000 = 250Copyrighted by Pearson24Evaluating Safety Inventory Given Desired Fill RateESC= 250 = ss1FssssL+sLfssssL= ss1Fsss707+707fsss707250 = ss1NORMDI

20、ST(ss/ 707,0,1,1)+707NORMDIST(ss/ 707,0,1,0)Use GOALSEEK to find safety inventory ss = 67 boxesCopyrighted by Pearson25Evaluating Safety Inventory Given Desired Fill RateFigure 12-3Copyrighted by Pearson26Impact of Desired Product Availability and Uncertainty As desired product availability goes up

21、the required safety inventory increasesFill RateSafety Inventory97.5%6798.0%18398.5%32199.0%49999.5%767Table 12-1Copyrighted by Pearson27Impact of Desired Product Availability and Uncertainty Goal is to reduce the level of safety inventory required in a way that does not adversely affect product ava

22、ilability Reduce the supplier lead time L Reduce the underlying uncertainty of demand (represented by sD)Copyrighted by Pearson28Benefits of Reducing Lead TimeD = 2,500/week, sD = 800, CSL = 0.95ss=NORMSINV(CSL)LsD=NORMSINV(.95)9 800 = 3,948If lead time is reduced to one weekss=NORMSINV(.95) 1800 =1

23、,316If standard deviation is reduced to 400ss=NORMSINV(.95)9 400 =1,974Copyrighted by Pearson29Impact of Supply Uncertaintyon Safety Inventory We incorporate supply uncertainty by assuming that lead time is uncertainD: Average demand per period sD: Standard deviation of demand per periodL: Average l

24、ead time for replenishment sL: Standard deviation of lead timeDL=DL sL=LsD2+D2sL2Copyrighted by Pearson30Impact of Lead Time Uncertainty on Safety InventoryAverage demand per period, D = 2,500Standard deviation of demand per period, sD = 500 Average lead time for replenishment, L = 7 days Standard d

25、eviation of lead time, sL = 7 daysMean ddlt, DL = DL = 2,500 x 7 = 17,500Standard deviation of ddlt sL=LsD2+D2sL2=75002+2,500272=17,500Copyrighted by Pearson31Impact of Lead Time Uncertainty on Safety Inventory Required safety inventoryss=FS1(CSL)sL=NORMSINV(CSL)sL=NORMSINV(0.90)17,500= 22,491 hard

26、drivessLs sLss (units)ss (days)615,05819,2987.72512,57016,1096.44410,08712,9275.1737,6169,7603.9025,1726,6282.6512,8283,6251.4501,3231,6950.68Table 12-2Copyrighted by Pearson32Impact of Aggregationon Safety Inventory How does aggregation affect forecast accuracy and safety inventoriesDi:Mean weekly

27、demand in region i, i = 1, k si:Standard deviation of weekly demand in region i, i = 1, k rij:Correlation of weekly demand for regions i, j, 1 i j kCopyrighted by Pearson33Impact of Aggregationon Safety InventoryTotal safety inventory in decentralized option=FS1(CSL)Lsii=1kDC=Dii=1k; varDC()=si2+2ri

28、jsisjiji=1k;sDC=varDC()DC=kD sDC=ksDCopyrighted by Pearson34Impact of Aggregationon Safety InventoryRequire safety inventory on aggregation=FS1(CSL)LsDCi=1kHolding-cost savings on aggregation per unit sold=FS1(CSL)LHDCsisDCi=1kCopyrighted by Pearson35Impact of Aggregationon Safety Inventory The safe

29、ty inventory savings on aggregation increase with the desired cycle service level CSL The safety inventory savings on aggregation increase with the replenishment lead time L The safety inventory savings on aggregation increase with the holding cost H The safety inventory savings on aggregation incre

30、ase with the coefficient of variation of demand The safety inventory savings on aggregation decrease as the correlation coefficients increaseCopyrighted by Pearson36Impact of Aggregationon Safety Inventory The Square-Root LawFigure 12-4Copyrighted by Pearson37Impact of Correlation on Value of Aggreg

31、ationStandard deviation of weekly demand, sD = 5; Replenishment, L = 2 weeks; Decentralized CSL = 0.9Total required safety inventory,ss=kFs1(CSL)LsD= 4Fs1(0.9)2 5= 4NORMSINV(0.9)2 5 = 36.24 carsAggregate r = 0sDC=4 5 =10Standard deviation of weekly demand at central outlet,ss=Fs1(0.9)LsDC=NORMSINV(0

32、.9)2 10 =18.12Copyrighted by Pearson38Impact of Correlation on Value of Aggregationr rDisaggregate Safety InventoryAggregate Safety Inventory036.2418.120.236.2422.920.436.2426.880.636.2430.320.836.2433.411.036.2436.24Table 12-3Copyrighted by Pearson39Impact of Correlation on Value of Aggregation Two

33、 possible disadvantages to aggregation1. Increase in response time to customer order2. Increase in transportation cost to customerCopyrighted by Pearson40Trade-offs of Physical Centralization Use four regional or one national distribution centerD = 1,000/week, sD = 300, L = 4 weeks, CSL = 0.95Total

34、required safety inventory,ss= 4Fs1(CSL)LsD= 4NORMSINV(0.95)4 300 = 3,948Four regional centersCopyrighted by Pearson41Trade-offs of Physical Centralization One national distribution center, r = 0sDC=4 300 = 600Standard deviation of weekly demand,ss=Fs1(0.95)LsDC=NORMSINV(0.95)4 600 =1,974Decrease in

35、holding costs = (3,948 1,974) $1,000 x 0.2 = $394,765Decrease in facility costs = $150,000Increase in transportation = 52 x 1,000 x (13 10) = $624,000Copyrighted by Pearson42Information Centralization Online systems that allow customers or stores to locate stock Improves product availability without

36、 adding to inventories Reduces the amount of safety inventoryCopyrighted by Pearson43Specialization Inventory is carried at multiple locations Should all products should be stocked at every location? Required level of safety inventory Affected by coefficient of variation of demand Low demand, slow-m

37、oving items, typically have a high coefficient of variation High demand, fast-moving items, typically have a low coefficient of variationCopyrighted by Pearson44Impact of Coefficient of Variation on Value of AggregationMotorsCleanerInventory is stocked in each storeMean weekly demand per store201,00

38、0Standard deviation40100Coefficient of variation2.00.1Safety inventory per store132329Total safety inventory211,200526,400Value of safety inventory$105,600,000$15,792,000Inventory is aggregated at the DCMean weekly aggregate demand32,0001,600,000Standard deviation of aggregate demand1,6004,000Coeffi

39、cient of variation0.050.0025Aggregate safety inventory5,26413,159Value of safety inventory$2,632,000$394,770SavingsTotal inventory saving on aggregation$102,968,000$15,397,230Total holding cost saving on aggregation$25,742,000$3,849,308Holding cost saving per unit sold$15.47$0.046Savings as a percen

40、tage of product cost3.09%0.15%Table 12-4Copyrighted by Pearson45Product Substitution The use of one product to satisfy demand for a different product1. Manufacturer-driven substitutionAllows aggregation of demandReduce safety inventoriesInfluenced by the cost differential, correlation of demand2. Cu

41、stomer-driven substitutionAllows aggregation of safety inventoryCopyrighted by Pearson46Component Commonality Without common components Uncertainty of demand for a component is the same as for the finished product Results in high levels of safety inventor With common components Demand for a componen

42、t is an aggregation of the demand for the finished products Component demand is more predictable Component inventories are reducedCopyrighted by Pearson47Value of Component Commonality27 PCs, 3 components, 3 x 27 = 81 distinct componentsMonthly demand = 5,000Standard deviation = 3,000Replenishment l

43、ead time = 1 monthCSL = 0.95= 81NORMSINV(0.95) 13,000= 399,699 unitsTotal safety inventory required=NORMSINV(0.95) 19 3,000=14,804 unitsSafety inventory per common componentCopyrighted by Pearson48Value of Component Commonality With component commonality Nine distinct components= 914,804 =133,236Tot

44、al safety inventory requiredCopyrighted by Pearson49Value of Component CommonalityNumber of Finished Products per ComponentSafety InventoryMarginal Reduction in Safety InventoryTotal Reduction in Safety Inventory1399,6992282,630117,069117,0693230,76651,864168,9334199,84930,917199,8505178,75121,09822

45、0,9486163,17615,575236,5237151,07212,104248,6278141,3159,757258,3849133,2338,082266,466Table 12-5Copyrighted by Pearson50Postponement Delay product differentiation or customization until closer to the time the product is sold Have common components in the supply chain for most of the push phase Move

46、 product differentiation as close to the pull phase of the supply chain as possible Inventories in the supply chain are mostly aggregateCopyrighted by Pearson51PostponementFigure 12-5Copyrighted by Pearson52Value of Postponement100 different paint colors, D = 30/week, sD = 10,L = 2 weeks, CSL = 0.95

47、Total required safety inventory,ss=100Fs1(CSL)LsD=100NORMSINV(0.95)2 10 = 2,326sDC=100 10 =100Standard deviation of base paint weekly demand,ss=Fs1(CSL)LsDC=NORMSINV(0.95)2 100 = 233Copyrighted by Pearson53Impact of Replenishment Policies on Safety Inventory Continuous Review PoliciesD:Average demand per period sD: Standard deviation of demand per periodL:Average lead time for replenishmen