1. Sport Obermeyer Case
John H. Vande Vate
Fall, 2009 1

2. Issues Learning Objectives:
How to measure demand uncertainty from disparate forecasts
How to accommodate uncertainty in sourcing
Low cost, high commitment, low flexibility (“contract”)
Higher cost, low commitment, higher flexibility (“spot”) 2

3. Finding the Right Mix Managing uncertainty
Low cost, high commitment, low flexibility (“contract”)
Higher cost, low commitment, higher flexibility (“spot”) 3

4. 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 4

5. 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 5

6. 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) 6

7. The Product
Gender
Styles
Colors
Sizes
Total Number of SKU’s: ~800 7

8. Service Deliver matching collections simultaneously
Deliver early in the season 8

9. Production Planning Example
Rococo Parka
Wholesale price $112.50
Average profit 24%* = $27
Average loss (Cost – Salvage)
8%* = $9 9

10. Sample Problem Why 2? It has worked
Forecast is average of the “experts” forecasts
Std dev of demand about forecast is 2x std dev of forecasts
Why 2? It has worked 10

11. Alternate Approach Issues? Keep records of Forecast and Actual sales
Construct a distribution of ratios Actual/Forecast
Assume next ratio will be a sample from this distribution
Item
Forecast
Actual Sales
Abs Error
Error Ratio 1
4349
100% - 2
1303
3454
165%
2.65 3
3821
7452
95%
1.95 4
4190
6764
61%
1.61 5
1975
713
64%
0.36 6
4638
4991 8%
1.08 7
1647
519
68%
0.32 8
2454
2030
17%
0.83 9
4567
8210
80%
1.80 10
1747
1350
23%
0.77 11
4824
4572 5%
0.95 12
1628
855
47%
0.53 13
942
1265
34%
1.34 14
3076
1681
45%
0.55 15
2173
2485
14%
1.14 16
1167
743
36%
0.64 17
2983
3388 18
4746
1512 19
2408
3163
31%
1.31 20
3126
3643
1.17 21
1000
894
11%
0.89 22
3457
3709 7%
1.07 23
4636
6233
Issues? 11

12. What might you expect to see in this distribution?
Alternate Approach
Historical ratios of Actual/Forecast
Error Ratio < 1, when forecast is too high
Error Ratio > 1, when forecast is too low
What might you expect to see in this distribution? 12

13. Getting a Distribution
Generate a point forecast via the usual process
Apply the historical distribution of A/F ratios to this point forecast.
Multiply by the forecast 13

14. Basics: Selecting an Order Quantity
News Vendor Problem
Order Q
Look at last item, what does it do for us?
Increases our (gross) profits (if we sell it)
Increases our losses (if we don’t sell it)
Expected impact?
Gross Profit*Chances we sell last item
Loss*Chances we don’t sell last item
Expected impact
P = Probability Demand < Q
(Selling Price – Cost)*(1-P)
(Cost – Salvage)*P
Expected reward: Why 1-P?
Expected risk: Why P? 14

15. Question How much to order? Expected impact
P = Probability Demand < Q
Reward: (Selling Price – Cost)*(1-P)
Risk: (Cost – Salvage)*P
How much to order? 15

16. If Salvage Value is > Cost?
How Much to Order
Balance the Risks and Rewards
Reward: (Selling Price – Cost)*(1-P)
Risk: (Cost – Salvage)*P
(Selling Price – Cost)*(1-P) = (Cost – Salvage)*P
P =
If Salvage Value is > Cost? 16

17. Calculating Gross Profits
Need to calculate Expected Sales
That takes some work
If demand x is Less than Q, we sell x
If demand x is Greater than Q, we sell Q 17

18. We’ll use 8% of wholesale and 24% of wholesale across all products
For Obermeyer
Ignoring all other constraints recommended target stock out probability is:
= 8%/(24%+8%) = 25%
We’ll use 8% of wholesale and 24% of wholesale across all products 18

19. Simplify our discussion
Every product has
Gross Profit = 24% of wholesale price
Cost – Salvage = 8% of wholesale price
Use Normal distribution for demand
Mean is the average forecast
Std dev is 2X the std. dev. of the forecasts 19

20. 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 20

21. Constraints Make at least 10,000 units in initial phase
Minimum Order Quantities 21

22. Invested Capital
The landed cost (to get product to Obermeyer) is the “investment”
Gross profit margin also nets out distribution costs – get the product to the customer
We’ll assume Invested Capital is 53.4% of wholesale price (as in Rococo 60.08/ = 53.4%) 22

23. Objective for the “first 10K”
Return on Investment:
Questions:
What happens to Expected Profit per unit as the order quantity increases?
What happens to the Invested Capital per unit as the order quantity increases?
What happens to Return on Investment as the order quantity increases?
Expected Profit
Invested Capital 23

24. Alternative Approach
Maximize Expected Profits over the season by simultaneously deciding early and late order quantities
See Fisher and Raman Operations Research 1996
Requires us to estimate before the Vegas show what our forecasts will be after the show. 24

25. First Phase Objective Maximize l = Can we exceed return l*? Is
Expected Profit
Invested Capital
Maximize l =
Can we exceed return l*? Is
L(l*) = Max Expected Profit - l*Invested Capital > 0?
Think of as an “interest” payment to shareholders for the invested capital. What’s the highest rate of interest we can support? 25

26. First Phase Objective:
Expected Profit
S ciQi
Maximize l =
Can we achieve return l?
L(l) = Max Expected Profit - lSciQi > 0?
The capital: ci is the landed cost/unit of product i 26

27. Investment What goes into ci ? Consider Rococo example
Investment 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
Question: Relationship to 24% profit margin? Why not 46.7% Gross Profit Margin?
Assumption: The cost difference (53.4%-46.15%) translates into additional profit for goods made in China (31.25% = ) 27

28. Summary
Hong Kong
Landed Cost = 53.4% of Wholesale price
Profit = 24% of Wholesale price
Distribution Cost = 22.6% of Wholesale price
Salvage Value = 68% of Wholesale price
If we don’t sell an item, we lose our investment of 53.4% % = 76% of wholesale price, but recoup 68% in salvage value. So, net we lose 8% of wholesale price
Assumption: Distribution cost is not part of invested capital 28

29. Solving for Qi For l fixed, how to solve
L(l) = Maximize S Expected Profit(Qi) - l S ciQi
s.t. Qi  0
Note it is separable (separate decision for each item)
Exactly the same thinking!
Last item:
Reward: Profit*Probability Demand exceeds Q
Risk: (Cost – Salvage)* Probability Demand falls below Q l?
l is like a tax rate on the investment that adds lci to the cost. 29

30. Hong Kong: Solving for Qi
Last item:
Reward: (Revenue – Cost – lci)*Prob. Demand exceeds Q
Risk: (Cost + lci – Salvage) * Prob. Demand falls below Q
As though Cost increased by lci
Balance the two
(Revenue – Cost – lci)*(1-P) = (Cost + lci – Salvage)*P
So P = (Profit – lci)/(Revenue - Salvage)
= Profit/(Revenue - Salvage) – lci/(Revenue - Salvage)
In our case
(Revenue - Salvage) = 32% Revenue,
Profit = 24% Revenue
ci = 53.4% Revenue
So P = 0.75 – l53.4%/32% = 0.75 – l
Recall that P is….
How does the order quantity Q change with l? 30

31. Q as a function of l Q l 31

32. Let’s Try It
Min Order Quantities! 32

33. Summary
China
Landed Cost = 46.15% of Wholesale price
Profit = 31.25% of Wholesale price
Distribution Cost = 22.6% of Wholesale price
Salvage Value = 68% of Wholesale price
If we don’t sell an item, we lose our investment of 46.15% % = 68.75% of wholesale price, but recoup 68% in salvage value. So, net we lose 0.75% of wholesale price 33

34. In China: Solving for Q Last item: Balance the two
Reward: (Revenue – Cost – lci)*Prob. Demand exceeds Q
Risk: (Cost + lci – Salvage) * Prob. Demand falls below Q
As though Cost increased by lci
Balance the two
(Revenue – Cost – lci)*(1-P) = (Cost + lci – Salvage)*P
So P = (Profit – lci)/(Revenue - Salvage)
= Profit/(Revenue - Salvage) – lci/(Revenue - Salvage)
In our case
(Revenue - Salvage) = 32% Revenue,
Profit = 31.25% Revenue
ci = 46.15% Revenue
So P = 31.25/32 – l46.15%/32% = – 1.442l
Recall that P is….
How does the order quantity Q change with l? 34

35. And China?
57% vs 36%
Min Order Quantities! 35

36. And Minimum Order Quantities
Maximize S Expected Profit(Qi) - l SciQi
M*zi  Qi  600*zi (M is a “big” number)
zi binary (do we order this or not)
If zi =0 we order 0
If zi =1 we order at least 600 36

37. Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lciQi
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 – lci)/(Revenue - Salvage)
(call it Q*)
Which is larger Expected Profit(Q*) – lciQ* or 0? 37

38. The return at the minimum order quantity!
Which is Larger?
What is the largest value of l for which, Expected Profit(Q*) – lciQ* > 0?
Expected Profit(Q*)/ciQ* > l
Expected Return on Investment if we make Q* > l
What is this bound?
The return at the minimum order quantity! 38

39. Return at Min Order Quantity
Remember computing the gross profits takes some work, we have to calculate the expected sales
Used a version of the ESC formula to calculate it
That integral requires some work 39

40. Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lciQi
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? 40

41. Adding a Lower Bound Q l 41

42. Expected Profit(Qi) - lciQi
Solving for zi
Li(l) = Maximize Expected Profit(Qi) - lciQi
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) - lciQi
So, if Expected Profit(Qi) – lciQi > 0, zi is 1
Once Q reaches its lower bound, Li(l) decreases, when it reaches 0, zi changes to 0 and remains 0
Li(l) reaches 0 when l is the return on 600 units. 42

43. If everything is made in one place, where would you make it?
Answers
Hong Kong
China 43

44. Where to Produce? 44

45. Next Push vs Pull Make-to-stock vs Make-to-order
Read “To Pull or Not to Pull: What is the Question?” by Hopp and Spearman 45