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Sport Obermeyer Case

Sport Obermeyer Case

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Sport Obermeyer Case

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  1. Sport Obermeyer Case John H. Vande Vate Spring, 2007 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 • 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” • 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. Production Planning Example • Rococo Parka • Wholesale price $112.50 • Average profit 24%*112.50 = $27 • Average loss 8%*112.50 = $9 8

  9. Sample Problem 9

  10. Alternate 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 Issues? 10

  11. Alternate Approach What might you expect to see in this distribution? • Historical ratios of Actual/Forecast Error Ratio < 1, when forecast is too high Error Ratio > 1, when forecast is too low 11

  12. Getting a Distribution • Generate a point estimate via usual process • Apply the historical distribution of A/F ratios to this point forecast. 12

  13. 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 Expected risk 13

  14. Question • Expected impact • P = Probability Demand < Q • Reward: (Selling Price – Cost)*(1-P) • Risk: (Cost – Salvage)*P • How much to order? 14

  15. 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? 15

  16. For Obermeyer • Ignoring all other constraints recommended target stock out probability is: = 8%/(24%+8%) = 25% 16

  17. 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 17

  18. Constraints • Make at least 10,000 units in initial phase • Minimum Order Quantities 18

  19. Objective for the “first 10K” • Return on Investment: Expected Profit Invested Capital 19

  20. First Phase Objective Expected Profit Invested Capital • Maximize t = • Can we exceed return t*? • Is L(t*) = Max Expected Profit - t*Invested Capital > 0? 20

  21. First Phase Objective: Expected Profit S ciQi • Maximize l = • Can we achieve return l? • L(l) = Max Expected Profit - lSciQi > 0? 21

  22. Investment • What goes into ci ? • Consider Rococo example • Investment is $60.08 on Wholesale Price of $112.50 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 (54.4%-46.15%) translates into additional profit for goods made in China (32.25% =24+8.25) 22

  23. Solving for Qi • For l fixed, how to solve L(l) = Maximize S Expected Profit(Qi) - lS 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 changes cost from lci to the cost. • Note that ci is not the Cost. It doesn’t include many expenses post receipt. 23

  24. 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 increase 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 – 1.66875l Recall that P is…. How does the order quantity Q change with l? 24

  25. Q as a function of l Q l 25

  26. Let’s Try It Min Order Quantities! 26

  27. 57% vs 36% And China? Min Order Quantities! 27

  28. And Minimum Order Quantities Maximize S Expected Profit(Qi) - lSciQi 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 28

  29. 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? 29

  30. 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 Investmentif we make Q* > l • What is this bound? 30

  31. 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 Li(l) = Maximize Expected Profit(Qi) - lciQi s.t. Qi  600 How does Qi change with l? 31

  32. Adding a Lower Bound Q l 32

  33. Objective Function • How does Objective Function change with l? Li(l) = Maximize Expected Profit(Qi) – lciQi 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 33

  34. 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. 34

  35. Answers Hong Kong If everything is made in one place, where would you make it? China 35

  36. Where to Produce? 36

  37. Other issues? • Aggressive view of Risk: Maximum Return • Other issues not addressed? • Other measures of risk? 37