1. Newsvendor Models & the Sport Obermeyer Case
John H. Vande Vate
Spring, 2012 1

2. Issues Learning Objectives:
We’ve discussed how to measure demand uncertainty based on historical forecast accuracy
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. More Generally Contracts with Carriers Labor Capacity Inventory
Assured capacity via contracts
Meet volatile demand with spot
Labor
Full-time employees
Over-time
Temporary workers
Capacity
Internal “owned”
Outsourced
Inventory
Safety Lead Time
Expedited Shipments 4

5. Obermeyer’s 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 5

6. 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 6

7. 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) 7

8. The Product
Gender
Styles
Colors
Sizes
Total Number of SKU’s: ~800 8

9. Service Deliver matching collections simultaneously
Deliver early in the season 9

10. Production Planning Example
Rococo Parka
Wholesale price $112.50
Average profit 24%* = $27
Cost = 76%* = $85.50
Average loss (Cost – Salvage)
8%* = $9
Salvage = (1-24%-8%)*112.50
= (1-32%)*112.50
= 68%*112.50
= $76.50 10

11. 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 11

12. Our Approach 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 12

13. Distribution of Demand
We have an estimated distribution of demand (however we get it)
Example Gail
Mean 1,017 units
Standard deviation 388 units
Question: How many items to order? 13

14. ObermeyerData.xls Margin %* (1-Margin %)* Price Price*Order Qty
(1-Margin %-Loss %)*
Price
Incr. Rev./Cost
Min(Order Qty, Actual Demand)*
Price
Revenue + Salvage - Cost
Max(0, Order Qty-Actual Demand)*
Salvage Value 14

15. What’s the Right Answer?
There is no “right” order quantity, we don’t know what demand will be
What’s the right approach to choosing an answer? 15

16. Meaningful Objective
Maximize the Expected Profit? 16

17. Marginal ROIC Marginal Expected Profit Marginal Invested Capital
Marginal Return on Investment:
Questions:
What happens to Marginal Expected Profit per unit as the order quantity increases?
What happens to the Marginal Invested Capital as the order quantity increases?
What happens to Marginal Return on Investment as the order quantity increases?
What order Quantity maximizes Marginal Return on Investment?
Which styles will show the higher Marginal Return on Investment?
Marginal Expected Profit
Marginal Invested Capital 17

18. 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, the Cycle Service Level
(Selling Price – Cost)*(1-P)
(Cost – Salvage)*P
Expected reward: Why 1-P?
Expected risk: Why P? 18

19. 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? 19

20. 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? 20

21. How Much to Order What does this mean? For Gail: P =
Selling Price – Cost = 24%Price
Selling Price – Salvage
= Selling Price – Cost + Cost – Salvage
= 24% Price + 8%Price
= 32% Price
P = 24/32 = 75%
What does this mean? 21

22. 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 22

23. 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
Every product has recommended P = 0.75
What does this mean? 23

24. 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 24

25. Does this make sense?
Why not do this? 25

26. P = 0.75 Explain the strategy Which products are riskier?
Which are safer? 26

27. Constraints Make at least 10,000 units in initial phase
Minimum Order Quantities
What issues should we consider in choosing what to make in the initial phase?
What objective to consider when choosing what to make in the initial phase? 27

28. Invested Capital
The landed cost (to get product to Obermeyer) is the “investment”
We’ll assume Invested Capital is Cost
Cost = (1-24%)*Price = 76% Price 28

29. Objective for the “first 10K”
Invest first in those items with the highest marginal return
Questions:
What happens to Marginal Expected Profit per unit as the order quantity increases?
What happens to the Marginal Invested Capital per unit as the order quantity increases?
What happens to Marginal Return on Investment as the order quantity increases?
Which styles will show the higher Marginal Return on Investment?
Marginal Expected Profit
Marginal Invested Capital 29

30. 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. 30

31. First Phase
Allocate the next units to the SKU with the highest marginal ROIC
Stop when we’ve allocated all 10,000 units 31

32. First Phase Objective:
ci is the invested capital (cost) per unit
For a given MROIC
Max Expected Profit – MROIC SciQi
The objective is separable
Max Expected Profit(Qi)-MROIC*ciQi
Set derivative to 0
Marginal Expected Profit - MROIC*ci = 0
MROIC =
Marginal Expected Profit
Marginal Invested Capital 32

33. First Phase Objective:
We find Qi so that
Marginal Expected Profit - MROIC*ci = 0
= MROIC
What does this mean about each unit we order?
Marginal Expected Profit(Qi)
Marginal Invested Capital 33

34. Solving Adjust MROIC until SQi = 10,000 Why =? How to accomplish this?34

35. Ordering
As though we
Sorted the units of the different skus in decreasing order of marginal ROIC
Took the top 10,000 35

36. Solving for Qi For MROIC fixed, how to solve
Maximize S Expected Profit(Qi) - MROIC S ciQi
s.t. Qi  0
Remember it is separable (separate decision for each item)
Exactly the same thinking as the News Vendor
Last item:
Reward: Profit*Probability Demand exceeds Q
Risk: (Cost – Salvage)* Probability Demand falls below Q
MROIC?
MROIC is like a tax or interest on the investment that adds
MROIC * ci to the cost. We pay it whether the item sells or
not.
If it sells, get the original profit – MROIC* ci
If it doesn’t sell, get (Salvage – Cost – MROIC*ci) 36

37. Solving for Qi Last item: Reward: Risk:
(Revenue – Cost – MROIC*ci)*Prob. Demand exceeds Q
(Revenue – Cost – MROIC*ci)*(1-P)
Risk:
(Cost + MROIC*ci – Salvage) * Prob. Demand falls below Q
(Cost + MROIC*ci – Salvage) * P
As though Cost increased by MROIC*ci , the “Tax” or “Interest” we pay to investors 37

38. Hong Kong: Solving for Qi
Balance the two
(Revenue – Cost – MROIC*ci)*(1-P) =
(Cost + MROIC*ci – Salvage)*P
So P = (Profit – MROIC*ci)/(Revenue - Salvage)
P = Profit/(Revenue - Salvage) – MROIC*ci/(Revenue - Salvage)
What happens to P as MROIC increases?
What happens to Qi as MROIC increases? 38

39. Summary
Hong Kong
Cost = 76% of Wholesale price
Profit = 24% of Wholesale price
Salvage Value = 68% of Wholesale price
If we don’t sell an item, we lose our investment of 76% of wholesale price, but recoup 68% in salvage value. So, net we lose 8% of wholesale price 39

40. Hong Kong: Solving for Qi
So P = (Profit – ROIC*ci)/(Revenue - Salvage)
= Profit/(Revenue - Salvage) – ROIC*ci/(Revenue - Salvage)
In our case
(Revenue - Salvage) = 32% Revenue,
Profit = 24% Revenue
ci = 76% Revenue
So P = 0.75 – MROIC*76%/32%
= 0.75 – 2.375*MROIC 40

41. Q as a function of MROIC Q
ROIC 41

42. Let’s Try It
Min Order Quantities! 42

43. Summary
China
Cost = 68.75% of Wholesale price
Profit = 31.25% of Wholesale price
Salvage Value = 68% of Wholesale price
If we don’t sell an item, we lose our investment of 68.75% of wholesale price, but recoup 68% in salvage value. So, net we lose 0.75% of wholesale price 43

44. In China: Solving for Q In our case So P = 31.25/32 – MROIC*68.75%/32%
So P = (Profit – MROIC*ci)/(Revenue - Salvage)
= Profit/(Revenue - Salvage) – MROIC*ci/(Revenue - Salvage)
In our case
(Revenue - Salvage) = 32% Revenue,
Profit = 31.25% Revenue
ci = 68.75% Revenue
So P = 31.25/32 – MROIC*68.75%/32%
= – 2.148*MROIC 44

45. 38.73% vs 25.5%
And China?
Min Order Quantities!
Why the same? 45

46. And Minimum Order Quantities
In Hong Kong:
As we drive up the MROIC, what’s happening to Qi?
When Qi reaches 600 (the lower bound), what do we know about
Marginal Expected Profit
Marginal Investment
What should happen to Qi for values of MROIC higher than this? 46

47. If everything is made in one place, where would you make it?
Answers
Hong Kong
China 47

48. Summary
Simple question of how much to make (no minimums, no issues of before or after the Vegas show)
Maximize expected profit
That’s just a newsvendor problem
Trade off risk of lost sales vs risk of salvage
Decide which 10,000 to make before show (no minimums, no choice of where to make them)
Highest marginal return on invested capital 48

49. Summary Impose minimums (no choice of where to make them)
If the tax rate exceeds the MROIC at the minimum order quantity, don’t make the product. Otherwise, make at least the minimum order quantity
Where to make the product?
China
Hong Kong 49

50. 1 if
We don’t make the product in China and MROIC is < Marginal Return at 600
Where to Produce?
If a style is not attractive to produce in China, it might be attractive in HK at the lower MOQ… 50

51. Idea It’s attractive to make it in Hong Kong if
The marginal return on 1,200 in China is lower than the tax rate (we don’t want to make it there)
but the marginal return on 600 in Hong Kong is higher than the tax rate (so it’s still attractive to make it there)
That doesn’t happen.
But what if we had to make 20,000 before the show? 51

52. With a 20K Target 52