Forecasting and Logistics

1
Forecastingand Logistics

• John H. Vande Vate
• Fall, 2002

2
Basics

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

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
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
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
Measuring Risk and Return

• Profit from the last item
• profit if demand is greater, 0 otherwise
• Expected Profit
• profitProbability demand is greater than our
  choice
• Risk posed by last item
• risk if demand is smaller, 0 otherwise
• Expected Risk
• riskProbability demand is smaller than our
  choice
• Example risk Salvage Value - Cost
• What if Salvage Value gt Cost?

7
Balancing Risk and Reward

• Expected Profit
• profitProbability demand is greater than our
  choice
• Expected Risk
• riskProbability demand is smaller than our
  choice
• How are probabilities Related?

8
Risk Reward
Our choice
How are they related?
9
Balance

• Expected Revenue
• profit(1- Probability demand is smaller than
  our choice)
• Expected Risk
• riskProbability demand is smaller than our
  choice
• Set these equal
• profit(1-P) -riskP
• profit (profit-risk)P
• profit/(profit - risk) P Probability demand
  is smaller than our choice

10
Making the Choice
Our choice
Cumulative Probability
profit/(profit - risk)
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

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)

13
Some Intuition

• Profit 1, Risk -1
• Mean 1000, Std Dev 100
• Whats the best strategy?

Order the average. Return 920 Why less than
1,000?
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?

15
Extend Idea

• Ship too little, you have to expedite the rest
• Expedite Cost
• Ship Q
• If demand lt Q
• We sell demand and salvage (Q demand)
• If demand gt Q
• We sell demand and expedite (demand Q)
• Whats the strategy?

16
Same idea

• Ignore profit from sales thats 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

Stock on hand
Lead Time
Reorder Point
Actual Lead Time Demand
Order placed
Avg LT Demand
Safety Stock
Time
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

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?

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
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 contd

• 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

29
(No Transcript)