Safety Stock

1. For in-class discussion: Read pages: 287-291 and 302-312 Safety Stock Managing Uncertainty in Supply Chain Safety Inventory

2. Safety Inventory Safety inventory (safety stock) is the inventory carried for purpose of satisfying demand that exceeds amount forecasted in a given period. You have forecasted demand next week to be 150 units? How many units do you order for next week?

3. Measuring Demand Variability • Recall,Observed demand (O)= systematic component (S) + Random Component ® • Use forecasting to determine systematic component • Random component is measure of demand uncertainty (requires use of safety stock) • How do we find random component? • Use historical demand data What was demand last year? Year before that? But… That gives observed demand, which is only useful if demand has no trend, no seasonality. 2. Use historical forecast error data

4. How to measure variability • Variance, σ2 • Measure of the “spread” of a distribution • Standard Deviation, σ • Square root of variance • Coefficient of variation • Relative measure

5. Continuous Review versus Periodic Review Inventory Models • Continuous Review: Inventory tracked continuously. When inventory hits ROP, order Q units. • Periodic Review: Inventory status checked at regular intervals. Place order to return inventory to some given level. • Also makes sense if can only order periodically (e.g., once a week, twice a month, etc.). “Reorder Point”: what we want to find. Cycle inventory (can use EOQ to approximate)

6. Lead Time Lead time (L) is the gap between when an order is placed and when it is received. We often carry safety stock because of demand uncertainty during a lead time. Expected Demand During Lead Time, DL Standard Deviation During Lead Time, σL

7. Evaluating Inventory Policy • How well are we doing? • Product fill rate (fr): fraction of product demand satisfied from product available in inventory • Probability that product demand is satisfied from available inventory. • Expected Shortage per Cycle (ESC): average units of demand not satisfied from inventory in a replenishment cycle • Cycle Service Level (CSL): fraction of replenishment cycles that end with all customer demand being met • “The probability of not having a stock-out in a replenishment cycle” – this is a pass or fail even if it is only one unit you still “failed” to avoid stockouts.

8. New Inventory Profile (Continuous Review) Units Q ROP Cycle Inventory = Q/2 Safety Inventory Time L Cycle

9. What’s Really Happening?(Continuous Review) Inventory Q Q Q ROP Time L L L Cycles not equal

10. 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 Continuous Review Formulas Average Inventory = Q/2 + ss

11. Calculating Safety Inventory(Continuous Review) Example: Weekly demand for product is normally distributed with mean 2500 and standard deviation 500. Manufacturer takes two weeks to fill an order. Currently you order 10,000 products when inventory hits 6,000. What is your safety inventory and average amount of inventory?

12. How to Calculate Cycle Service Level? CSL = Prob(demand during lead time ≤ ROP) =NORMDIST(ROP,DL, σL,1) Example:Weekly demand for Palm Pilots is normally distributed with mean 2,500 and standard deviation 500. Replenishment lead time is 2 weeks. What is CSL if you order 10,000 Palm Pilots whenever inventory reaches 6,000? DL=D X L= 2500X 2=5000 σL= σD √ L=500 √ 2=707 SCL=NORMDIST(6000,5000,707,1)=.92

13. What if I don’t have Excel? NORMDIST is the Excel command to calculate the PDF or CDF for a given Normal Distribution Standard Deviation Tells Excel whether To calculate PDF or CDF: 0 means PDF 1 means CDF Mean 5000 6000

14. Without Excel (cont) NORMDIST (Finding CDF) Without Excel: Use Standard Normal Table 1. Transform to Standard Normal: 2. Lookup Value in Table: 0.9207

15. How to find Fill Rate? • First find Expected Shortage per Replenishment Cycle (ESC), then find fill rate. Example (cont): What is fill rate in previous example where Q =10,000, DL = 5,000, sL = 707, and ROP = 6,000? Notice that in your book in page 294 this is written as ss[1-NORMDIST(…). There are two problems with this: Excels does not recognize implicit multiplication or “brackets”, [ or ]. You must write this as: ss*(1-NORMDIST(…)

16. More Important: How to figure out how much safety inventory needed? • To Meet a Given Cycle Service Level (Without Excel) Lookup in standard normal table • Find z value for given CSL • (standard normal table) • 2. ss = zsL m z

17. Example From previous example: Without Excel: ss = zsL 1. Find z value (Look up 0.92 in standard normal table) z = 1.41 2. ss = 1.41*707 = 996.87

18. To Meet a Given Fill Rate • Calculate ESC for desired fill rate, ESC = (1 – fr)Q • Find ss that solves following equation in Excel: How? Use Goal Seek in Excel. Data-What if analysis – Goal Seek – or for older excel versions: Tools | Goalseek For previous example compute the ss if the desired fill rate is 0.999.

19. Periodic Review • Inventory levels reviewed and orders placed after time T (review interval) • Bring inventory up to an order up-to level (OUL) • Size of order may vary • Depends on demand during previous reorder interval • Still have lead time of L • OUL set so that • Prob(demand during L+T≤OUL=CSL)

20. Periodic Review Formulas L: Lead time T: Reorder interval D : Average demand per unit time DT+L : Average demand during (T+L) time periods D: Standard deviation of demand per unit time L+T: Standard deviation of demand during L+T periods CSL: Cycle service level ss: Safety inventory OUL: Order up to level -periodic review requires higher level of safety inventory than continuous review. WHY?

21. Periodic Review Example Every month Steel Works, Inc. places orders for the raw material it uses in making its custom steel applications. Once an order is placed, it takes about 2 weeks to arrive from the supplier. Weekly demand for this raw material is normally distributed with a mean of 1,000 tons and a standard deviation of 200 tons. How many tons of raw material should Steel Works, Inc. carry in safety stock to maintain a 95% CSL? What is order up-to level? Ss=zsT+L=NORMSINV(CSL)xsT+L =NORMSINV(0.95)x489.9=805.81 tons OUL=DT+L+ss =6000+805.81=6805.81 tons

22. Example: Periodic Review Policy D= 2,500/week; D= 500 L = 2 weeks; T = 4 weeks; CSL = 0.90 What is the required safety inventory and OUL? Dt+l=(T+L)D=6x2500=15000 T+L =√ (T+L) D= √6*500=1225 Ss=normsinv(.0)*1225=1570 boxes OUL=Dd+L +ss=15000+1570=16570 Factors driving safety inventory • Demand uncertainty • Replenishment lead time • Reorder interval

23. 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

24. Impact of Supply Uncertainty D = 2,500/day; D= 500 L = 7 days; Q = 10,000; CSL = 0.90 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 inventory 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

25. Basic Quick Response Initiatives • Reduce information uncertainty in demand • Reduce replenishment lead time • Reduce supply uncertainty or replenishment lead time uncertainty

26. Accurate Response: The Impact of Inventory Pooling

27. Factors Affecting Value of Aggregation • Demand Correlation • Coefficient of Variation of demand • Value of product

28. Impact of Correlation on Benefit From Aggregation

29. Impact of cv and Product Value on Benefit From Aggregation

30. Methods of Accurate Response • Physical Centralization • Information centralization • Specialization • Product substitution • Raw material commonality (postponement)

31. Example: Value of Component Commonality