Safety Stock

1. 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 (R) • 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. Assuming Normally Distributed Forecast Errors A Shortcut: • Calculate forecast errors, Et • Calculate Mean Square Error • Calculate standard deviation of random errors Then demand distribution is: Normal(μ, σ) From forecast • (Normally distributed with mean, μ, and standard deviation, σ)

6. 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)

7. 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 DL = Standard Deviation During Lead Time, σL

8. 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

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

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

11. 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

12. 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? SS? Avg. Inv.? D = 2,500 u/week Sigma = 500 u/week L= 2 weeks Q= 10,000 (EoQ) RoP= 6,000 RoP= Dl + SS DL = (D)(L) = (2,500)(2) = 5,000 6000 = 5,000 + SS SS = 1,000 Avg Inventory = Q/2 + SS 10,000/2 + 1000 Avg Inv= 6,000

13. How to Calculate Cycle Service Level? CSL = Prob(demand during lead time ≤ ROP) Example:Weekly demand for iphonesis normally distributed with mean 2,500 and standard deviation 500. Replenishment lead time is 2 weeks. What is CSL if you order 10,000 iphoneswhenever inventory reaches 6,000?

14. 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

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

16. 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 course pack 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(…)

17. 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

18. 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

19. 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.

20. 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

21. 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

22. 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?

23. 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? Factors driving safety inventory • Demand uncertainty • Replenishment lead time • Reorder interval

24. 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

25. 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

26. Risk Pooling Strategies • A risk pooling strategy redesigns the supply chain, the production process, or the product so the firm can mitigate the consequences of uncertainty • Four types of risk pooling: • Location pooling • Product pooling • Lead time pooling • Delayed differentiation • Consolidated distribution • Capacity pooling

27. 1) Location Pooling DC DC • Can be used to decrease inventory while holding service level constant, or increase service level while holding inventory costs. • Ex. Nordstrom: • pooling in-store and online inventories across the entire company using IT systems and inventory transshipments • Sales increased by 39% due to stock-out reduction and reduced delivery lead times R R1 R2 R3

28. 1) Location Pooling… • Pros. • Reduces demand uncertainty therefore reducing inventory. • Increases service levels • Cons: • May move inventory away from customers • May increase delivery lead time / transportation costs • Alternatives: • Virtual pooling

29. 2) Product Pooling • Ex. Hewlett-Packard (Europe) • Deskjet-Plus printers manufactured in Vancouver • Three DCs in N.A., Europe, and Asia • Different power-supply modules/manuals needed to accommodate local requirements • One month delivery lead time • Solution: • Build one generic printer • Add power-supply modules/manuals for different counties only in response to demand

30. 2) Product Pooling… • Limitations: • A generic design may not provide key functionality to customers with special needs • A generic design may be more expensive to produce as it may require additional components • A generic design may eliminate brand/price segmentation opportunities

31. 3) Lead Time Pooling • Consolidated Distribution Supplier Supplier DC

32. 3) Lead Time Pooling • Delayed Differentiation Color pigments, paint mixing, packaging Retailer Color pigments paint mixing, packaging

33. Why Pooling? • Reduces uncertainty • Demand amount • Demand location • Lead time • Uncertainty reduction • Results in reduction of safety stock!

34. The Impact of Inventory Pooling

35. Factors Affecting Value of Inventory Pooling • Demand Correlation • Lower correlation favors pooling • Positive correlation can make pooling undesirable • Coefficient of Variation • Value of product

36. Impact of Correlation on Benefit From Aggregation

37. Example: Value of Component Commonality