Sport Obermeyer Case John H. Vande Vate Fall, 2009 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

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

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

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

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

Service Deliver matching collections simultaneously Deliver early in the season 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

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

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

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

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

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

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

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

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

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

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

Everyone has a 25% chance of stockout 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 20

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

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 60.08/112.50 = 53.4%) 22

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

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

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

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

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 (53.4%-46.15%) translates into additional profit for goods made in China (31.25% =24+7.25) 27

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 28

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

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 – 1.66875l Recall that P is…. How does the order quantity Q change with l? 30

Q as a function of l Q l 31

Let’s Try It Min Order Quantities! 32

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 33

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% = 0.977 – 1.442l Recall that P is…. How does the order quantity Q change with l? 34

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

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

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

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

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

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

Adding a Lower Bound Q l 41

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

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

Where to Produce? 44

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