Sport Obermeyer Case John H Vande Vate Spring

Sport Obermeyer Case John H. Vande Vate Spring, 2008 1 1

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 2

Finding the Right Mix • Managing uncertainty – Low cost, high commitment, low flexibility (“contract”) – Higher cost, low commitment, higher flexibility (“spot”) 3 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 4 4

Production Options • Hong Kong • Mainland (Guangdong, Lo Village) – More expensive – Smaller lot sizes – Faster – More flexible – Cheaper – Larger lot sizes – Slower – Less flexible 5 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 6

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

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

Production Planning Example • • Rococo Parka Wholesale price $112. 50 Average profit 24%*112. 50 = $27 Average loss (Cost – Salvage) 8%*112. 50 = $9 9 9

Sample Problem 10 10

Alternate Approach • Keep records of Forecast and Actual Issues? sales • Construct a distribution of ratios Actual/Forecast • Assume next ratio will be a sample from this distribution Item Forecast Actual Sales Abs Error Ratio 1 4349 0 100% 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 9 10 11 12 13 14 15 2454 4567 1747 4824 1628 942 3076 2173 2030 8210 1350 4572 855 1265 1681 2485 17% 80% 23% 5% 47% 34% 45% 14% 0. 83 1. 80 0. 77 0. 95 0. 53 1. 34 0. 55 1. 14 16 17 18 19 20 21 22 23 1167 2983 4746 2408 3126 1000 3457 4636 743 3388 1512 3163 3643 894 3709 6233 36% 14% 68% 31% 17% 11% 7% 34% 0. 64 1. 14 0. 32 1. 31 1. 17 0. 89 1. 07 1. 34 11 11

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

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

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

Question • Expected impact ØP = Probability Demand < Q ØReward: (Selling Price – Cost)*(1 -P) ØRisk: (Cost – Salvage)*P • How much to order? 15 15

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

For Obermeyer • Ignoring all other constraints recommended target stock out probability is: = 8%/(24%+8%) = 25% 17 17

Ignoring Constraints Everyone has a 25% chance of stockout Everyone orders Mean + 0. 6745 s P =. 75 [from. 24/(. 24+. 08)] Probability of being less than Mean + 0. 6745 s is 0. 75 18 18

Constraints • Make at least 10, 000 units in initial phase • Minimum Order Quantities 19 19

Objective for the “first 10 K” • Return on Investment: Expected Profit Invested Capital • 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? 20 20

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. 21 21

First Phase Objective • Maximize t = Expected Profit Invested Capital • Can we exceed return t*? • Is L(t*) = Max Expected Profit - t*Invested Capital > 0? 22 22

First Phase Objective: Expected Profit • Maximize l = S c i Qi • Can we achieve return l? • L(l) = Max Expected Profit - l. Sci. Qi > 0? 23 23

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 (31. 25% =24+7. 25) 24 24

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% + 22. 6% = 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 25 25

Solving for Qi • For l fixed, how to solve L(l) = Maximize S Expected Profit(Qi) - l S ci. Qi 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. 26 26

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 – l 53. 4%/32% = 0. 75 – 1. 66875 l Recall that P is…. How does the order quantity Q change with l? 27 27

Q as a function of l Q l 28 28

Let’s Try It Min Order Quantities! 29 29

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% + 22. 6% = 68. 75% of wholesale price, but recoup 68% in salvage value. So, net we lose 0. 75% of wholesale price 30 30

In China: Solving for Q • 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 = 31. 25% Revenue – ci = 46. 15% Revenue So P = 31. 25/32 – l 46. 15%/32% = 0. 977 – 1. 442 l Recall that P is…. How does the order quantity Q change with l? 31 31

57% vs 36% And China? Min Order Quantities! 32 32

And Minimum Order Quantities Maximize S Expected Profit(Qi) - l Sci. Qi 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 33 33

Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lci. Qi 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*) – lci. Q* or 0? 34 34

Which is Larger? • What is the largest value of l for which, Expected Profit(Q*) – lci. Q* > 0? • Expected Profit(Q*)/ci. Q* > l • Expected Return on Investment if we make Q* > l • What is this bound? 35 35

Solving for Q’s Li(l) = Maximize Expected Profit(Qi) - lci. Qi 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) - lci. Qi s. t. Qi 600 How does Qi change with l? 36 36

Adding a Lower Bound Q l 37 37

Objective Function • How does Objective Function change with l? Li(l) = Maximize Expected Profit(Qi) – lci. Qi We know Expected Profit(Qi) is concave As l increases, Q decreases and so does the Expected Profit When Q hits lower bound, it remains there. After that Li(l) decreases linearly 38 38

Solving for zi Li(l) = Maximize Expected Profit(Qi) - lci. Qi 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) - lci. Qi So, if Expected Profit(Qi) – lci. Qi > 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. 39 39

Answers Hong Kong If everything is made in one place, where would you make it? China 40 40

Where to Produce? 41 41

Related Projects • Two projects explore these issues – FMCG: Fleet Composition • Own-fleet vs 3 rd party fleet – Pharma: CRO Sourcing • Contract vs spot 42 42

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 43 43