1、11-1,Chapter 11Managing Uncertainty in theSupply Chain: Safety Inventory,Supply Chain Management(3rd Edition),11-2,Role of Inventory in the Supply Chain,Cost,Availability,Efficiency,Responsiveness,11-3,Outline,The role of safety inventory in a supply chain Determining the appropriate level of safety

2、 inventory Impact of supply uncertainty on safety inventory Impact of aggregation on safety inventory Impact of replenishment policies on safety inventory Managing safety inventory in a multi-echelon supply chain Estimating and managing safety inventory in practice,11-4,Measuring Demand Uncertainty,

3、Inventory,Time,CycleInventory,Cycle,Lead time (L),Reorder point (ROP),Demand (D),Order quantity/lot size (Q),11-5,Measuring Demand Uncertainty,Inventory,Time,AverageInventory,CycleInventory,SafetyInventory,Cycle,Lead time (L),Reorder point (ROP),Demand (D),Order quantity/lot size (Q),11-6,The Role o

4、f Safety Inventory in a Supply Chain,Forecasts are rarely completely accurate If average demand is 1000 units per week, then half the time actual demand will be greater than 1000, and half the time actual demand will be less than 1000; what happens when actual demand is greater than 1000? If you kep

5、t only enough inventory in stock to satisfy average demand, half the time you would run out Safety inventory,11-7,What is Safety Inventory?,Safety inventory Safety inventory is inventory carried for the purpose of satisfying demand that exceeds the amount forecasted for a given period Safety invento

6、ry is the average inventory remaining when the replenishment lot arrives,11-8,Role of Safety Inventory,Average inventory is therefore cycle inventory plus safety inventory There is a fundamental tradeoff: Raising the level of safety inventory provides higher levels of product availability and custom

7、er service Raising the level of safety inventory also raises the level of average inventory and therefore increases holding costs Very important in high-tech or other industries where obsolescence is a significant risk (where the value of inventory, such as PCs, can drop in value) Compaq and Dell in

8、 PCs,11-9,Two Key Questions when Planning Safety Inventory,(1) What is the appropriate level of safety inventory to carry? (2) What actions can be taken to improve product availability while reducing safety inventory?,11-10,Determining the AppropriateLevel of Safety Inventory,Measuring demand uncert

9、ainty Measuring product availability Replenishment policies Evaluating cycle service level and fill rate Evaluating safety level given desired cycle service level or fill rate Impact of required product availability and uncertainty on safety inventory,11-11,Determining Appropriate Level of Safety In

10、ventory,The appropriate level of safety inventory is determined by the following three factors The uncertainty of both demand and supply Higher levels of uncertainty require higher levels of safety inventory given a particular desired level of product availability The desired level of product availa

11、bility Higher levels of desired product availability require higher levels of safety inventory given a particular level of uncertainty The replenishment policy Different replenishment policies lead to different levels of safety inventory,11-12,Measuring Demand Uncertainty,Demand has a systematic com

12、ponent and a random component The estimate of the random component is the measure of demand uncertainty Random component is usually estimated by the standard deviation of demand Notation: D = Average demand per period sD = standard deviation of demand per period L = lead time = time between when an

13、order is placed and when it is received Uncertainty of demand during lead time is what is important,11-13,Measuring Demand Uncertainty,P = demand during k periods = kD W = std dev of demand during k periods = sRSqrt(k) Coefficient of variation = cv = m/s = mean/(std dev) = size of uncertainty relati

14、ve to demand,11-14,Measuring Demand Uncertainty,Inventory,Time,AverageInventory,CycleInventory,SafetyInventory,Cycle,Lead time (L),Reorder point (ROP),Demand (D),Demand during lead time DL = LD,Order quantity/lot size (Q),Standard deviation of demand over lead time L = (L)D,11-15,Measuring Product A

15、vailability,Cycle service level (CSL) Fraction of replenishment cycles that end with all customer demand met Product fill rate (fr) Fraction of demand that is satisfied from product in inventory Probability that product demand is supplied from available inventory Order fill rate Fraction of orders t

16、hat are filled from available inventory,11-16,CSL and fr are different!,11-17,Replenishment Policies,Replenishment policy: decisions regarding when to reorder and how much to reorder Continuous review Periodic review,11-18,Replenishment Policies,Continuous review Inventory is continuously monitored

17、and an order of size Q is placed when the inventory level reaches the reorder point (ROP) Periodic review Inventory is checked at regular (periodic) intervals and an order is placed to raise the inventory to a specified threshold, the order-up-to level (OUL),11-19,Safety Inventory,What actions can b

18、e taken to improve product availability while reducing safety inventory?,Why is it that successful retailers and manufacturers (i.e. Wal-Mart, Seven-Eleven Japan, Dell) carry only little inventory but still have high levels of product availability?,11-20,Continuous Review Policy: Safety Inventory an

19、d Cycle Service Level,L:Lead time for replenishment D:Average demand per unit time D:Standard deviation of demand per period DL: Mean demand during lead time L: Standard deviation of demand during lead time CSL: Cycle service level ss: Safety inventory ROP: Reorder point,Average Inventory = Q/2 + ss

20、,11-21,Example 11-1: Evaluating safety inventory given an inventory policy,Reorder point (ROP) = demand during lead time + safety inventory= DL + ss Average flow time = (avg. inventory) / (avg. demand),ROP = DL + ss,11-22,Example 11.1: Estimating Safety Inventory (Continuous Review Policy),D = 2,500

21、/week; D = 500 L = 2 weeks; Q = 10,000; ROP = 6,000 DL = DL = (2500)(2) = 5000 ss = ROP - DL = 6000 - 5000 = 1000 Cycle inventory = Q/2 = 10000/2 = 5000 Average Inventory = cycle inventory + ss = 5000 + 1000 = 6000 Average Flow Time = Avg inventory / throughput = 6000/2500 = 2.4 weeks,11-23,Example

22、11-2: Evaluating cycle service level given a replenishment policy,Weekly demand for Palms is normally distributed, with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks. Assume that the demand is independent from one week to the next. Evaluate the CSL resulti

23、ng from a policy of ordering 10,000 Palms when there are 6,000 Palms in inventory,11-24,Example 11-2: Evaluating cycle service level given a replenishment policy,Inventory,Time,0,Reorder point,11,000,6,000,1,000,CSL = Prob(of not stocking out in a cycle),Lead time,= Prob(demand during lead time ROP)

24、,11-25,Measuring Demand Uncertainty,Inventory,Time,AverageInventory,CycleInventory,SafetyInventory,Cycle,Lead time (L),Reorder point (ROP),Demand (D),Order quantity/lot size (Q),Demand during lead time DL = LD,Standard deviation of demand over lead time L = (L)D,11-26,Example 11-2: Evaluating cycle

25、service level given a replenishment policy,CSL = Prob(demand during lead time ROP),11-27,Example 11-2: Evaluating cycle service level given a replenishment policy,CSL = Prob(demand during lead time ROP),CSL = F(ROP,DL,L),11-28,Example 11.2: Estimating Cycle Service Level (Continuous Review Policy),D

26、 = 2,500/week; D = 500 L = 2 weeks; Q = 10,000; ROP = 6,000 Cycle service level, CSL = F(DL + ss, DL, L) = = NORMDIST (DL + ss, DL, L) = NORMDIST(6000,5000,707,1) = 0.92 (This value can also be determined from a Normal probability distribution table),11-29,Example 11-4: Evaluating safety inventory g

27、iven a desired service level,LD = 2*2,500 = 5,000,SQRT(L)D = SQRT(2)*500 = 707,F(ROP, DL, L) = F(6000, 5000, 707) = 0.92,F(ROP, DL, L) = NORMDIST(ROP, DL, L, 1),11-30,Fill Rate,Proportion of customer demand satisfied from stock Stockout occurs when the demand during lead time exceeds the reorder poi

28、nt ESC is the expected shortage per cycle (average demand in excess of reorder point in each replenishment cycle) ss is the safety inventory Q is the order quantity,ESC = -ss1-NORMDIST(ss/L, 0, 1, 1) + L NORMDIST(ss/L, 0, 1, 0),11-31,Product Fill Rate,Q = 1000,11-32,Example 11.3: Evaluating Fill Rat

29、e,ss = 1,000, Q = 10,000, sL = 707, Fill Rate (fr) = ? ESC = -ss1-NORMDIST(ss/L, 0, 1, 1) + L NORMDIST(ss/L, 0, 1, 0) = -1,0001-NORMDIST(1,000/707, 0, 1, 1) + 707 NORMDIST(1,000/707, 0, 1, 0) = 25.13 fr = (Q - ESC)/Q = (10,000 - 25.13)/10,000 = 0.9975,11-33,Factors Affecting Fill Rate,Safety invento

30、ry: Fill rate increases if safety inventory is increased. This also increases the cycle service level. Lot size: Fill rate increases on increasing the lot size even though cycle service level does not change.,11-34,Example 11.4: EvaluatingSafety Inventory Given CSL,D = 2,500/week; D = 500 L = 2 week

31、s; Q = 10,000; CSL = 0.90 DL = 5000, L = 707 (from earlier example) ss = FS-1(CSL)L = NORMSINV(0.90)(707) = 906 (this value can also be determined from a Normal probability distribution table) ROP = DL + ss = 5000 + 906 = 5906,11-35,Evaluating Safety InventoryGiven Desired Fill Rate,D = 2500, sD = 5

32、00, Q = 10000 If desired fill rate is fr = 0.975, how much safety inventory should be held? ESC = (1 - fr)Q = 250 Solve,11-36,Evaluating Safety Inventory Given Fill Rate (try different values of ss),11-37,Ethical Dilemma,Wayne Hills Hospital in Wayne, Nebraska, faces a problem common to large urban

33、hospitals, as well as to small remote ones as itself. That problem is deciding how much of each type of whole blood to keep in stock. Because blood is expensive and has a limited shelf life, Wayne Hills naturally wants to keep its stocks as low as possible. Unfortunately, past disasters such as a ma

34、jor tornado and a train wreck demonstrated that lives would be lost when not enough blood was available to handle massive needs.,Source: Operations Management, J. Heizer and B. Render,11-38,Impact of Required Product Availability and Uncertainty on Safety Inventory,Desired product availability (cycl

35、e service level or fill rate) increases, required safety inventory increases Demand uncertainty (sL) increases, required safety inventory increases Managerial levers to reduce safety inventory without reducing product availability reduce supplier lead time, L (better relationships with suppliers) re

36、duce uncertainty in demand, sL (better forecasts, better information collection and use),11-39,Impact of Supply Uncertainty,D: Average demand per period D: Standard deviation of demand per period L: Average lead time sL: Standard deviation of lead time,11-40,Impact of Supply Uncertainty,D = 2,500/da

37、y; D = 500 L = 7 days; Q = 10,000; CSL = 0.90; sL = 7 days DL = DL = (2500)(7) = 17500 ss = Fs-1 (CSL)sL = NORMSINV(0.90) x 17550 = 22,491,11-41,Impact of Supply Uncertainty,Safety inventory when sL = 0 is 1,695 Safety inventory when sL = 1 is 3,625 Safety inventory when sL = 2 is 6,628 Safety inven

38、tory when sL = 3 is 9,760 Safety inventory when sL = 4 is 12,927 Safety inventory when sL = 5 is 16,109 Safety inventory when sL = 6 is 19,298,11-42,Impact of Aggregationon Safety Inventory,Models of aggregation Information centralization Specialization Product substitution Component commonality Pos

39、tponement,11-43,Impact of Aggregation,11-44,Impact of Aggregation(Example 11.7),Car Dealer : 4 dealership locations (disaggregated) D = 25 cars; sD = 5 cars; L = 2 weeks; desired CSL=0.90 What would the effect be on safety stock if the 4 outlets are consolidated into 1 large outlet (aggregated)? At

40、each disaggregated outlet: For L = 2 weeks, sL = 7.07 cars ss = Fs-1(CSL) x sL = Fs-1(0.9) x 7.07 = 9.06 Each outlet must carry 9 cars as safety stock inventory, so safety inventory for the 4 outlets in total is (4)(9) = 36 cars,11-45,Impact of Aggregation(Example 11.7),One outlet (aggregated option

41、): RC = D1 + D2 + D3 + D4 = 25+25+25+25 = 100 cars/wk sRC = Sqrt(52 + 52 + 52 + 52) = 10 sLC = sDC Sqrt(L) = (10)Sqrt(2) = (10)(1.414) = 14.14 ss = Fs-1(CSL) x sLC = Fs-1(0.9) x 14.14 =18.12 or about 18 cars If r does not equal 0 (demand is not completely independent), the impact of aggregation is n

42、ot as great (Table 11.3),11-46,Impact of Aggregation,If number of independent stocking locations decreases by n, the expected level of safety inventory will be reduced by square root of n (square root law) Many e-commerce retailers attempt to take advantage of aggregation (Amazon) compared to bricks

43、 and mortar retailers (Borders) Aggregation has two major disadvantages: Increase in response time to customer order Increase in transportation cost to customer Some e-commerce firms (such as Amazon) have reduced aggregation to mitigate these disadvantages,11-47,Information Centralization,Virtual ag

44、gregation Information system that allows access to current inventory records in all warehouses from each warehouse Most orders are filled from closest warehouse In case of a stockout, another warehouse can fill the order Better responsiveness, lower transportation cost, higher product availability,

45、but reduced safety inventory Examples: McMaster-Carr, Gap, Wal-Mart,11-48,Specialization,Stock all items in each location or stock different items at different locations? Different products may have different demands in different locations (e.g., snow shovels) There can be benefits from aggregation Benefits of aggregation can be affected by: coefficient of variation of demand (higher cv yields greater reduction in safety inventory from centralization) value of item (high value items provide more benefits from centralization) Table 11.4,11-49,Value of Aggregation at Grainger (Table 11.4