Forecasting
and
Logistics
John H. Vande Vate
Fall, 2002
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1
Fundamental Rules
• The farther in the future we must forecast,
the worse the forecast
• The longer we have to do something the
cheaper it is to do it.
• Balance these two
– Long plans mean bad forecasts
– Short plans mean high operational costs
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2
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 = revenue)
• Question: What value do you choose?
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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?
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Measuring Risk and Return
• Profit from the last item
 $p if the Outcome is greater,$0 otherwise
• Expected Profit
 $p*Probability Outcome is greater than our choice
• Risk posed by last item
 $r if the Outcome is smaller, $0 otherwise
• Expected Risk
 $r*Probability Outcome is smaller than our choice
Example: r = Cost – Salvage Value
What if r < 0?
What if Salvage Value > Cost?
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Balancing Risk and Reward
• Expected Profit
$p*Probability Outcome is greater than
our choice
• Expected Risk
$r*Probability Outcome is smaller than
our choice
• How are probabilities Related?
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Risk & Reward
Distribution
0.45
Prob. Outcome is smaller
0.4
Our choice
0.35
How are they
related?
0.3
Prob. Outcome is larger
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
12
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7
Balance
• Expected Revenue
 $p*(1- Probability Outcome is smaller than our choice)
• Expected Risk
 $r*Probability Outcome is smaller than our choice
• Set these equal
p*(1-P) = r*P
p = (r+p)*P
p/(r + p) = P = Probability Outcome is smaller than our
choice
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Making the Choice
Distribution
0.45
0.4
Prob. Outcome is smaller
Our choice
0.35
0.3
Cumulative
Probability
0.25
0.2
p/(r+p)
0.15
0.1
0.05
0
0
2
4
6
8
10
12
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9
How does this Apply?
• Source in Asia
– Cost is Low, Lead time is high (add 2 wks)
• Source in Mexico
– Cost is higher, lead time is lower
• Place your first order far in advance in Asia. Asia
has capacity
• Place subsequent order in Mexico when you
know more
• What do you order from Asia?
• What do you order from Mexico?
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What Matters?
• Ordering from Asia
– Expected Demand from?
– Variance in Demand from?
• Ordering from Mexico
– What you ordered from Asia
– Expected Demand
– Variance in Demand
Anything Else?
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What Else!
How much you can learn from waiting!
If the forecast is bad before and bad after you
might as well order early
If the forecast is bad before but good after,
you gain by waiting.
But, how to know….
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Example: Common Variance
Order x(k) of product k
Products differ only in mean demand
Can’t order more than 5,000 from Asia
Express x(k) = (k) + z*
Probability Demand < x(k)?
Normal (x(k) - (k))/) = Normal(z)
So?
Use News Vendor to find z
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Only Means Matter
Product
Profit
1
2
3
4
5
Risk
110
110
110
110
110
25
25
25
25
25
Total
Mean
Std
1000
1000
1500
2500
1000
7000
200
200
200
200
200
P*
z
Order Q P(z*)
Order
0.814815 0.89578 1179.156 0.02275
600
0.814815 0.89578 1179.156
600
0.814815 0.89578 1679.156
1100
0.814815 0.89578 2679.156
2100
0.814815 0.89578 1179.156
600
Total Order 7895.78
5000
Max Order
5000
Target z*
-2
x(k) = (k) + z*
S x(k) = S ((k) + z*) = 5,000
n*z* = 5,000 - S (k)
z = (5,000 - S (k))/(n*)
Then find x(k) from z.
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Sourcing Decisions
• What matters:
–
–
–
–
–
–
Piece price
Quality
Freight
Packaging
Pipeline inventory
Etc
• And Now:
– Leadtime impacts on forecast accuracy and
– Forecast accuracy impacts on supply chain costs!
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Where Else?
• Where else do these ideas apply?
• What if we are the manufacturer?
• The longer it takes us to make a
product, the farther forward we must
forecast
• What can we do to reduce this?
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