Forecasting and Logistics

1. Forecastingand Logistics John H. Vande Vate Fall, 2002 1

2. Basics • Read the text for forecasting basics • Will not spend class time on the mechanics 2

3. Fundamental Rules • Rule #1: The farther in the future we must forecast, the worse the forecast • The longer we have available to do something the cheaper it is to do it. • Balance these two • Long plans mean bad forecasts • Short plans mean high operational costs 3

4. Balancing Risk • News vendor problem • A single shot at a fashion market • Guess how much to order • If you order too much, you can only salvage the excess (perhaps at a loss) (s-c = net salvage value) • If you order too little, you lose the opportunity to sell (r-c = profit) • Question: What value do you choose? 4

5. The Idea • Balance the risks • Look at the last item • What did it promise? • What risk did it pose? • If Promise is greater than the risk? • If the Risk is greater than the promise? 5

6. Measuring Risk and Return • Profit from the last item • $profit if demand is greater, $0 otherwise • Expected Profit • $profit*Probability demand is greater than our choice • Risk posed by last item • $risk if demand is smaller, $0 otherwise • Expected Risk • $risk*Probability demand is smaller than our choice Example: risk = Salvage Value - Cost What if Salvage Value > Cost? 6

7. Balancing Risk and Reward • Expected Profit • $profit*Probability demand is greater than our choice • Expected Risk • $risk*Probability demand is smaller than our choice • How are probabilities Related? 7

8. Prob. Outcome is smaller Prob. Outcome is larger Risk & Reward Our choice How are they related? 8

9. Balance • Expected Revenue • $profit*(1- Probability demand is smaller than our choice) • Expected Risk • $risk*Probability demand is smaller than our choice • Set these equal • profit*(1-P) = -risk*P • profit = (profit-risk)*P • profit/(profit - risk) = P = Probability demand is smaller than our choice 9

10. Prob. Demand is smaller Making the Choice Our choice Cumulative Probability profit/(profit - risk) 10

11. Example • What we sell in the month, we earn $1 per unit on • If we hold a unit in inventory past the end of the month, we lose $0.50 because of price falls and inventory costs • Demand forecasted as N(m, s) • s measures our uncertainty 11

12. What to do? • How much to ship • Last item • If we sell it • Earn $1 with probability that demand exceeds amount • (1-P) • If we fail to sell it • Pay $0.50 with probability that demand falls short • -0.5P • So, we want P to be 1/(1+.5) = 2/3 ~ .67 • Go look that up in the N(m, s) 12

13. Some Intuition • Profit = $1, Risk = -$1 • Mean = 1000, Std Dev = 100 • What’s the best strategy? Order the average. Return ~$920 Why less than $1,000? 13

14. What happens? • What happens to return as s • Increases? • Decreases? • What happens to s as lead time • Increases? • Decreases? • What happens to return as lead time • Increases? • Decreases? 14

15. Extend Idea • Ship too little, you have to expedite the rest • Expedite Cost • Ship Q • If demand < Q • We sell demand and salvage (Q – demand) • If demand > Q • We sell demand and expedite (demand – Q) • What’s the strategy? 15

16. Same idea • Ignore profit from sales – that’s independent of Q • Focus on salvage and expedite costs • Look at last item • Chance we salvage it is P • Chance we expedite it is (1-P) • Balance these costs • Unit salvage cost * P = Unit expedite cost (1-P) • P = expedite/(expedite + salvage) 16

17. Another View • Rule #2: The less detailed the subject matter, the more accurate the forecast 17

18. Safety Stock • Protection against variability • Variability in lead time and • Variability in demand, etc. • Typically described as days of supply • Should be described as standard deviations in lead time demand • Example: BMW safety stock • For axles only protects against lead time variability • For option parts protects against usage variability too 18

19. Traditional Basics • Basic tool to manage risk Stock on hand Lead Time Reorder Point Actual Lead Time Demand Order placed Avg LT Demand Safety Stock Time 19

20. Safety Stock Basics • n customers • Each with lead time demand N(m, s) • Individual safety stock levels • Choose z from N(0,1) to get correct probability that lead time demand exceeds z, • Safety stock for each customer is zs • Total safety stock is nzs 20

21. Safety Stock Basics • Collective Lead time demand N(nm, ns) • This is true if their demands and leadtimes are independent! • Collective safety stock is nzs • Typically demands are negatively or positively correlated • What happens to the collective safety stock if demands are • positively correlated? • Negatively correlated? 21

22. Inventory (Risk) Pooling The impact is less than the sqrt of 2 law It predicts that if 2 DCs need 47 units then a single DC will need 33 The impact is greater than the sqrt of 2 law It predicts that if 2 DCs need 5.5 units then a single DC will need 4 Pooling Inventory can reduce safety stock 22

23. Inventory (Risk) Pooling • Centralizing inventory can reduce safety stock • Best results with high variability and uncorrelated or negatively correlated demands • Postponement ~ risk pooling across products 23

24. Forecasting So What • Mechanics of forecasting • Review the past • Project it into the future • What to do with forecasts? • Build a business case with the means (planning) • Assess risks with the std deviations (hedging) • Real question is • Not how to forecast better, but • How to manage risk better 24

25. Examples • Inventory Strategy • What inventories (risks) can you pool • Supplying international operations • How much to ship • How much to expedite • How much inventory to hold • How to manage the process • International Sourcing • What products/volumes to source from fast, expensive local sources • What products/volumes to source from slow, long lead time distant sources 25

26. Examples cont’d • Purchasing Strategy • What to purchase on the “spot market” • What prices to fix with contracts • Manufacturing Strategy • What products/volumes to build-to-order • What products/volumes to build-to-stock • Our focus on supplying international operations 26

27. Supplying International Ops • Several interwoven issues • Assessing the risk • Reducing the risk through product/supply chain design • Managing the risks through effective supply process 27

28. Reducing the Risks • Focus on postponement • Postponement: Delaying the point of product differentiation 28

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