1 1 Forecasting and Logistics John H. Vande Vate Fall, 2002

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

3 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

4 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?

5 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?

6 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?

7 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?

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

9 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

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

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( ,  )  measures our uncertainty

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( ,  )

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?

14 What happens? What happens to return as  –Increases? –Decreases? What happens to  as lead time –Increases? –Decreases? What happens to return as lead time –Increases? –Decreases?

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?

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)

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

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

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

20 Safety Stock Basics n customers Each with lead time demand N( ,  ) 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 z  –Total safety stock is nz 

21 Safety Stock Basics Collective Lead time demand N(n ,  n  ) This is true if their demands and leadtimes are independent! Collective safety stock is  nz  Typically demands are negatively or positively correlated What happens to the collective safety stock if demands are –positively correlated? –Negatively correlated?

22 Inventory (Risk) Pooling Pooling Inventory can reduce safety stock 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

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

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

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

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

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

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

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