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

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

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

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

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

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

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

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

Service Deliver matching collections simultaneously Deliver early in the season 9

Production Planning Example Rococo Parka Wholesale price $112.50 Average profit 24%*112.50 = $27 Cost = 76%*112.50 = $85.50 Average loss (Cost – Salvage) 8%*112.50 = $9 Salvage = (1-24%-8%)*112.50 = (1-32%)*112.50 = 68%*112.50 = $76.50 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 11

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

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

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

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

Meaningful Objective Maximize the Expected Profit? 16

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

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

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

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

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

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

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

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 24

Does this make sense? Why not do this? 25

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Q as a function of MROIC Q ROIC 41

Let’s Try It Min Order Quantities! 42

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

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% = 0.977 – 2.148*MROIC 44

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

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

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

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

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

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

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

With a 20K Target 52