Sport Obermeyer

1
Sport Obermeyer

• What to order?
• What are the issues?

2
A Sample Problem

• Commit 10,000 units before show
• Commit 10,000 units after show
• Minimum of 600 units

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A First Approach

• Ignore differences in
• Profit margins
• Salvage values
• Ignore minimum lot sizes
• Consider only first order cycle

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Sample Problem
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Normal Distribution
Std Dev.s
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Idea 1

• Make all products equally likely to sell out
• Choose a single std dev. To set production quotas
  for all products

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What should the Std. Dev. Be?
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Normal Distribution
Set order Qty to this many std. devs
Probability we stock out Probability demand
exceeds over qty 0.86
Probability we discount last item Probability
demand is smaller than order quantity 0.14
Std Dev.s
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Whats Wrong with This?

• What else should we be looking at?
• Still just worried about
• Order up to 10,000
• One order cycle
• No minimum order qty.

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A Second Idea

• Look at 1 Product
• How to trade off risks of overstock (discounting)
  vs risks of understock (lost sales)?
• If we order Q
• The last item faces what risk of being
  discounted?
• Probability Demand lt Q F(Q)
• The last item faces what risk of selling out
• Probability Demand gt Q 1 - F(Q)

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We want to be indifferent

• We want two to be equal
• Expected loss from Overstock COF(Q)
• Expected loss from Lost Sale CL(1-F(Q))
• A little Algebra
• F(Q) CL/(COCL)

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Example

• Oversimplification
• Lost Sale CL Selling Price - Cost
• Discount CO Cost - Salvage Value
• Electra
• Selling Price 173
• Cost 50
• Salvage 0
• Lost Sale CL 123
• Discount CO 50
• Want Probability of Discount F(Q) 123/173
  0.71
• Find Q with this cumulative probability 2,599
  

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Balancing Risks
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Additional Thoughts

• Whats the derivative of the cost as a function
  of order quantity?
• Expected Cost of Discounting Last Item (increases
  with order size) - Expected Cost of Stocking Out
  (decreases with order size)
• Decrease Order with largest estimated derivative

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Estimated Derivative
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2-Rounds

• What additional Issues?
• What rules of thumb?
• Only order late
• Surely order early

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Differences in Suppliers

• Hong Kong
• Higher Cost
• Smaller Minimums
• Faster
• What rules of Thumb?