11

Forecastingand

Logistics

John H. Vande Vate

Fall, 2002

22

Basics

• Read the text for forecasting basics

• Will not spend class time on the mechanics

33

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

44

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?

55

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?

66

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 - CostWhat if Salvage Value > Cost?

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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?

88

Risk & RewardDistribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 2 4 6 8 10 12

Prob. Outcome is smaller

Prob. Outcome is larger

Our choice

How are they related?

99

Balance

• Expected Revenue$profit*(1- Probability demand is smaller than our

choice)

• Expected Risk$risk*Probability demand is smaller than our choice

• Set these equalprofit*(1-P) = -risk*Pprofit = (profit-risk)*Pprofit/(profit - risk) = P = Probability demand is smaller

than our choice

1010

Distribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 2 4 6 8 10 12

Making the Choice

Prob. Demand is smaller

Our choice

profit/(profit - risk)

Cumulative Probability

1111

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

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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(, )

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Some Intuition

• Profit = $1, Risk = -$1

• Mean = 1000, Std Dev = 100

• What’s the best strategy?

-0.0005

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0 200 400 600 800 1000 1200 1400

Order the average. Return~$920

Why less than $1,000?

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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?

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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?

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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)

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Another View

• Rule #2: The less detailed the subject matter, the more accurate the forecast

1818

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

1919

Traditional Basics

• Basic tool to manage risk

Time

Sto

ck o

n ha

nd

Safety Stock

Reorder Point

Order placed

Lead Time

Actual Lead Time Demand

Avg LT Demand

2020

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

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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?

2222

Inventory (Risk) PoolingHistorical Data for Product A

1 2 3 4 5 6 7 8Massachusetts 33 45 37 38 55 30 18 58New Jersey 46 35 41 40 26 48 18 55Pooled 79 80 78 78 81 78 36 113

Average Std DevCoeff of

Var

Avg. Lead time

DemandSafety Stock

Reorder Point EOQ

Order Up To Level

Avg. Inventory

Massachusetts 39.25 13.18 0.34 39.25 24.78 64 132 196 91New Jersey 38.63 12.05 0.31 38.63 22.66 61 131 192 88Pooled 77.88 20.71 0.27 77.88 38.95 117 186 303 132

Historical Data for Product B1 2 3 4 5 6 7 8

Massachusetts 0 2 3 0 0 1 3 0New Jersey 2 4 0 0 3 1 0 0Pooled 2 6 3 0 3 2 3 0

Average Std DevCoeff of

Var

Avg. Lead time

DemandSafety Stock

Reorder Point EOQ

Order Up To Level

Avg. Inventory

Massachusetts 1.13 1.36 1.21 1.13 2.55 4 22 26 14New Jersey 1.25 1.58 1.26 1.25 2.97 4 24 28 15Pooled 2.38 1.92 0.81 2.38 3.62 6 32 38 20

Inventory ComparisonMassachusetts New Jersey Total Pooled Reduction

Product A 91 88 179 132 26%Product B 14 15 28 20 30%Total 105 103 207 152 27%

Week

Week

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

2323

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

2424

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

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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

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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

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Supplying International Ops

• Several interwoven issues– Assessing the risk– Reducing the risk through product/supply

chain design– Managing the risks through effective supply

process

2828

Reducing the Risks

• Focus on postponement

• Postponement: Delaying the point of product differentiation

2929