Sport Obermeyer Case

1
Sport Obermeyer Case

• John H. Vande Vate
• Spring, 2006

2
Issues

• Question What are the issues driving this case?
• How to measure demand uncertainty from disparate
  forecasts
• How to allocate production between the factories
  in Hong Kong and China
• How much of each product to make in each factory

3
Describe the Challenge

• Long lead times
• Its November 92 and the company is starting to
  make firm commitments for its 93 94 season.
• Little or no feedback from market
• First real signal at Vegas trade show in March
• Inaccurate forecasts
• Deep discounts
• Lost sales

4
Production Options

• Hong Kong
• More expensive
• Smaller lot sizes
• Faster
• More flexible

• Mainland (Guangdong, Lo Village)
• Cheaper
• Larger lot sizes
• Slower
• Less flexible

5
The Product

• 5 Genders
• Price
• Type of skier
• Fashion quotient
• Example (Adult man)
• Fred (conservative, basic)
• Rex (rich, latest fabrics and technologies)
• Beige (hard core mountaineer, no-nonsense)
• Klausie (showy, latest fashions)

6
The Product

• Gender
• Styles
• Colors
• Sizes
• Total Number of SKUs 800

7
Service

• Deliver matching collections simultaneously
• Deliver early in the season

8
The Process

• Design (February 92)
• Prototypes (July 92)
• Final Designs (September 92)
• Sample Production, Fabric Component orders
  (50)
• Cut Sew begins (February, 93)
• Las Vegas show (March, 93 80 of orders)
• SO places final orders with OL
• OL places orders for components
• Alpine Subcons Cut Sew
• Transport to Seattle (June July)
• Retailers want full delivery prior to start of
  season (early September 93)
• Replenishment orders from Retailers

Quotas!
9
Quotas

• Force delivery earlier in the season
• Last man loses.

10
The Critical Path of the SC

• Contract for Greige
• Production Plans set
• Dying and printing
• YKK Zippers

11
Driving Issues

• Question What are the issues driving this case?
• How to measure demand uncertainty from disparate
  forecasts
• How to allocate production between the factories
  in Hong Kong and China
• How much of each product to make in each factory
• How are these questions related?

12
Production Planning Example

• Rococo Parka
• Wholesale price 112.50
• Average profit 24112.50 27
• Average loss 8112.50 9

13
Sample Problem
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Recall the Newsvendor

• Ignoring all other constraints recommended target
  stock out probability is
• 1-Profit/(Profit Risk)
• 8/(248) 25

15
Ignoring Constraints
Everyone has a 25 chance of stockout Everyone
orders Mean 0.6745s
P .75 from .24/(.24.08) Probability of being
less than Mean 0.6745s is 0.75
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Constraints

• Make at least 10,000 units in initial phase
• Minimum Order Quantities

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Objective for the first 10K

• First Order criteria
• Return on Investment
• Second Order criteria
• Standard Deviation in Return
• Worry about First Order first

Expected Profit Invested Capital
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First Order Objective
Expected Profit Invested Capital

• Maximize t
• Can we exceed return t?
• Is
• L(t) Max Expected Profit - tInvested Capital
  gt 0?

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First Order Objective

• Initially Ignore the prices we pay
• Treat every unit as though it costs Sport
  Obermeyer 1
• Maximize l
• Can we achieve return l?
• L(l) Max Expected Profit - lS Qi gt 0?

Expected Profit Number of Units Produced
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Solving for Qi

• For l fixed, how to solve
• L(l) Maximize S Expected Profit(Qi) - l S Qi
• s.t. Qi ? 0
• Note it is separable (separate decision each Q)
• Exactly the same thinking!
• Last item
• Profit ProfitProbability Demand exceeds Q
• Risk Loss Probability Demand falls below Q
• l?
• Set P (Profit l)/(Profit Risk)
• 0.75 l/(Profit Risk)

Error here let p be the wholesale price,
Profit 0.24p Risk 0.08p P (0.24p
l)/(0.24p 0.08p) 0.75 - l/(.32p)
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Solving for Qi

• Last item
• Profit ProfitProbability Demand exceeds Q
• RiskRisk Probability Demand falls below Q
• Also pay l for each item
• Balance the two sides
• Profit(1-P) l RiskP
• Profit l (Profit Risk)P
• So P (Profit l)/(Profit Risk)
• In our case Profit 24, Risk 8 so
• P .75 l/(.32Wholesale Price)
• How does the order quantity Q change with l?

Error This was omitted. It is not needed later
when we calculate cost as, for example,
53.4Wholesale price, because it factors out of
everything.
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Q as a function of l
Doh! As we demand a higher return, we can
accept less and less risk that the item wont
sell. So, We make less and less.
Q
l
23
Lets Try It
Min Order Quantities!
Adding the Wholesale price brings returns in line
with expectations if we can make 26.40 24 of
110 on a 1 investment, thats a 2640 return
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And Minimum Order Quantities

• Maximize S Expected Profit(Qi) - l SQi
• Mzi ? Qi ? 600zi (M is a big number)
• zi binary (do we order this or not)

If zi 1 we order at least 600
If zi 0 we order 0
25
Solving for Qs

• Li(l) Maximize Expected Profit(Qi) - lQi
• s.t. Mzi ? Qi ? 600zi
• zi binary
• Two answers to consider
• zi 0 then Li(l) 0
• zi 1 then Qi is easy to calculate
• It is just the larger of 600 and the Q that gives
  P (profit - l)/(profit risk) (call it Q)
• Which is larger Expected Profit(Q) lQ or 0?
• Find the largest l for which this is positive.
  For
• l greater than this, Q is 0.

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Solving for Qs

• Li(l) Maximize Expected Profit(Qi) - lQi
• s.t. Mzi ? Qi ? 600zi
• zi binary
• Lets first look at the problem with zi 1
• Li(l) Maximize Expected Profit(Qi) - lQi
• s.t. Qi ? 600
• How does Qi change with l?

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Adding a Lower Bound
Q
l
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Objective Function

• How does Objective Function change with l?
• Li(l) Maximize Expected Profit(Qi) lQi
• We know Expected Profit(Qi) is concave

As l increases, Q decreases and so does the
Expected Profit
When Q hits its lower bound, it remains there.
After that Li(l) decreases linearly
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The Relationships
Capital Charge Expected Profit
Q reaches minimum
Past here, Q 0
l/110
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Solving for zi

• Li(l) Maximize Expected Profit(Qi) - lQi
• s.t. Mzi ? Qi ? 600zi
• zi binary
• If zi is 0, the objective is 0
• If zi is 1, the objective is
• Expected Profit(Qi) - lQi
• So, if Expected Profit(Qi) lQi gt 0, zi is 1
• Once Q reaches its lower bound, Li(l) decreases,
  when it reaches 0, zi changes to 0 and remains 0

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Answers
Error That resolves the question of why we got a
higher return in China with no cost differences!
Hong Kong
China
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First Order Objective With Prices

• It makes sense that l, the desired rate of return
  on capital at risk, should get very high, e.g.,
  1240, before we would drop a product completely.
  The 1 investment per unit we used is
  ridiculously low. For Seduced, that 1 promises
  2473 17.52 in profit (if it sells). That
  would be a 1752 return!
• Lets use more realistic cost information.

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First Order Objective With Prices
Expected Profit S ciQi

• Maximize l
• Can we achieve return l?
• L(l) Max Expected Profit - lSciQi gt 0?
• What goes into ci ?
• Consider Rococo example
• Cost is 60.08 on Wholesale Price of 112.50 or
  53.4 of Wholesale Price. For simplicity, lets
  assume ci 53.4 of Wholesale Price for
  everything from HK and 46.15 from PRC

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Return on Capital
If everything is made in one place, where would
you make it?
Hong Kong
China
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Gail
Make it in China
Expected Profit above Target Rate of Return
Make it in Hong Kong
Stop Making It.
Target Rate of Return
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What Conclusions?

• There is a point beyond which the smaller minimum
  quantities in Hong Kong yield a higher return
  even though the unit cost is higher. This is
  because we dont have to pay for larger
  quantities required in China and those extra
  units are less likely to sell.
• Calculate the return of indifference (when
  there is one) style by style.
• Only produce in Hong Kong beyond this limit.

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Where to Make What?
That little cleverness was worth 2
Not a big deal. Make Gail in HK at minimum
38
What Else?

• Kais point about making an amount now that
  leaves less than the minimum order quantity for
  later
• Secondary measure of risk, e.g., the variance or
  std deviation in Profit.