1. John H. Vande Vate Spring, 2006
Sport Obermeyer Case
John H. Vande Vate
Spring, 2006 1

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 2

3. Describe the Challenge
Long lead times:
It’s November ’92 and the company is starting to make firm commitments for it’s ‘93 – 94 season.
Little or no feedback from market
First real signal at Vegas trade show in March
Inaccurate forecasts
Deep discounts
Lost sales 3

4. Production Options Hong Kong Mainland (Guangdong, Lo Village)
More expensive
Smaller lot sizes
Faster
More flexible
Mainland (Guangdong, Lo Village)
Cheaper
Larger lot sizes
Slower
Less flexible 4

5. The Product 5 “Genders” Example (Adult man) 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) 5

6. The Product
Gender
Styles
Colors
Sizes
Total Number of SKU’s: ~800 6

7. Service Deliver matching collections simultaneously
Deliver early in the season 7

8. The Process Quotas! 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! 8

9. Quotas
Force delivery earlier in the season
Last man loses. 9

10. The Critical Path of the SC
Contract for Greige
Production Plans set
Dying and printing
YKK Zippers 10

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? 11

12. Production Planning Example
Rococo Parka
Wholesale price $112.50
Average profit 24%* = $27
Average loss 8%* = $9 12

13. Sample Problem 13

14. 1-Profit/(Profit + Risk)
Recall the Newsvendor
Ignoring all other constraints recommended target stock out probability is:
1-Profit/(Profit + Risk)
=8%/(24%+8%) = 25% 14

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

16. Constraints Make at least 10,000 units in initial phase
Minimum Order Quantities 16

17. 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 17

18. First Order Objective Maximize t = Can we exceed return t*? Is
Expected Profit
Invested Capital
Maximize t =
Can we exceed return t*? Is
L(t*) = Max Expected Profit - t*Invested Capital > 0? 18

19. Number of Units Produced
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 > 0?
Expected Profit
Number of Units Produced 19

20. 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: Profit*Probability 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 = 0.24*p
Risk = 0.08*p
P = (0.24p – l)/(0.24p p)
= l/(.32p) 20

21. Solving for Qi Last item: Balance the two sides:
Profit: Profit*Probability Demand exceeds Q
Risk:Risk * Probability Demand falls below Q
Also pay l for each item
Balance the two sides:
Profit*(1-P) – l = Risk*P
Profit – l = (Profit + Risk)*P
So P = (Profit – l)/(Profit + Risk)
In our case Profit = 24%, Risk = 8% so
P = .75 – l/(.32*Wholesale 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, 53.4%*Wholesale price, because it factors out of everything. 21

22. Q as a function of l Q l Doh!
As we demand a higher return, we can accept
less and less risk that the item won’t sell. So,
We make less and less. Q l 22

23. Let’s 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, that’s a 2640% return 23

24. And Minimum Order Quantities
Maximize S Expected Profit(Qi) - l SQi
M*zi  Qi  600*zi (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 24

25. Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lQi
s.t. M*zi  Qi  600*zi
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. 25

26. Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lQi
s.t. M*zi  Qi  600*zi
zi binary
Let’s first look at the problem with zi = 1
s.t. Qi  600
How does Qi change with l? 26

27. Adding a Lower Bound Q l 27

28. As l increases, Q decreases and so does the Expected Profit
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 28

29. Capital Charge = Expected Profit
The Relationships
Capital Charge = Expected Profit
Q reaches minimum
Past here, Q = 0
l/110 29

30. Expected Profit(Qi) - lQi
Solving for zi
Li(l) = Maximize Expected Profit(Qi) - lQi
s.t. M*zi  Qi  600*zi
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 > 0, zi is 1
Once Q reaches its lower bound, Li(l) decreases, when it reaches 0, zi changes to 0 and remains 0 30

31. Answers Hong Kong China In China?
Error: That resolves the question of why we got a higher return in China with no cost differences!
Hong Kong
In China?
China 31

32. 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 24%*$73 = $17.52 in profit (if it sells). That would be a 1752% return!
Let’s use more realistic cost information. 32

33. First Order Objective: With Prices
Expected Profit
S ciQi
Maximize l =
Can we achieve return l?
L(l) = Max Expected Profit - lSciQi > 0?
What goes into ci ?
Consider Rococo example
Cost is $60.08 on Wholesale Price of $ or 53.4% of Wholesale Price. For simplicity, let’s assume ci = 53.4% of Wholesale Price for everything from HK and 46.15% from PRC 33

34. If everything is made in one place, where would you make it?
Return on Capital
If everything is made in one place, where would you make it?
Hong Kong
China 34

35. Gail Make it in China Make it in Hong Kong Stop Making It.
Expected Profit above Target Rate of Return
Make it in Hong Kong
Stop Making It.
Target Rate of Return 35

36. 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 don’t 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. 36

37. That little cleverness was worth 2%
Where to Make What?
That little cleverness was worth 2%
Not a big deal. Make Gail in HK at minimum 37

38. What Else?
Kai’s 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. 38