Download presentation
Presentation is loading. Please wait.
Published byDerick Skinner Modified over 9 years ago
1
1 1 Newsvendor Models & the Sport Obermeyer Case John H. Vande Vate Fall, 2011
2
2 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”)
3
3 3 Finding the Right Mix Managing uncertainty –Low cost, high commitment, low flexibility (“contract”) –Higher cost, low commitment, higher flexibility (“spot”)
4
4 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
5 5 Production Options Hong Kong –More expensive –Smaller lot sizes –Faster –More flexible Mainland (Guangdong, Lo Village) –Cheaper –Larger lot sizes –Slower –Less flexible
6
6 6 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)
7
7 7 The Product Gender –Styles –Colors –Sizes Total Number of SKU’s: ~800
8
8 8 Service Deliver matching collections simultaneously Deliver early in the season
9
9 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
10 Sample Problem 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
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 ItemForecastActual SalesAbs ErrorError Ratio 143490100% - 213033454165% 2.65 33821745295% 1.95 44190676461% 1.61 5197571364% 0.36 6463849918% 1.08 7164751968% 0.32 82454203017% 0.83 94567821080% 1.80 101747135023% 0.77 11482445725% 0.95 12162885547% 0.53 13942126534% 1.34 143076168145% 0.55 152173248514% 1.14 16116774336% 0.64 172983338814% 1.14 184746151268% 0.32 192408316331% 1.31 203126364317% 1.17 21100089411% 0.89 22345737097% 1.07 234636623334% 1.34
12
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
13 ObermeyerData.xls Margin %* Price (1-Margin %-Loss %)* Price (1-Margin %)* Price*Order Qty Min(Order Qty, Actual Demand)* Price Max(0, Order Qty-Actual Demand)* Price Revenue + Salvage - Cost Profit/Cost
14
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
15 Meaningful Objective Maximize the Expected Profit? Maximize Expected ROIC?
16
16 ROIC 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? –What order Quantity maximizes Return on Investment? –Which styles will show the higher return on investment? Expected Profit Invested Capital
17
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
18 Question Expected impact P = Probability Demand < Q Reward: (Selling Price – Cost)*(1-P) Risk: (Cost – Salvage)*P How much to order?
19
19 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
20 How Much to Order 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
21 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
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
23 Ignoring Constraints Everyone has a 25% chance of stockout Everyone orders Mean + 0.6745 P =.75 [from.24/(.24+.08)] Probability of being less than Mean + 0.6745 is 0.75
24
24 Does this make sense? Why not do this?
25
25 P = 0.75 Explain the strategy Which products are riskier? Which are safer?
26
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
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
28 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? –Which styles will show the higher return on investment? Expected Profit Invested Capital
29
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
30 First Phase Objective Maximize ROIC = Can we exceed a given ROIC*? Is L(ROIC*) = Max Expected Profit – ROIC* *Invested Capital > 0? Expected Profit Invested Capital Think of ROIC as an “interest” payment to shareholders for the invested capital. What’s the highest rate of interest we can support?
31
31 First Phase Objective: Maximize ROIC= Can we achieve return ROIC? L(ROIC) = Max Expected Profit – ROIC c i Q i > 0? Expected Profit c i Q i The capital: c i is the landed cost/unit of product i
32
32 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
33
33 Solving for Q i For ROIC fixed, how to solve L(ROIC) = Maximize Expected Profit(Q i ) - ROIC c i Q i s.t. Q i 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 –ROIC ROIC is like a tax rate on the investment that adds ROIC * c i to the cost. We pay it whether the item sells or not
34
34 Hong Kong: Solving for Q i Last item: –Reward: (Revenue – Cost – ROIC*c i )*Prob. Demand exceeds Q (Revenue – Cost – ROIC*c i )*(1-P) –Risk: (Cost + ROIC*c i – Salvage) * Prob. Demand falls below Q (Cost + ROIC*c i – Salvage) * P –As though Cost increased by ROIC*c i, the Tax we pay to investors
35
35 Hong Kong: Solving for Q i Balance the two (Revenue – Cost – ROIC*c i )*(1-P) = (Cost + ROIC*c i – Salvage)*P So P = (Profit – ROIC*c i )/(Revenue - Salvage) = Profit/(Revenue - Salvage) – ROIC*c i /(Revenue - Salvage) In our case –(Revenue - Salvage) = 32% Revenue, –Profit = 24% Revenue –c i = 76% Revenue So P = 0.75 – ROIC*76%/32% = 0.75 – 2.375*ROIC Recall that P is…. How does the order quantity Q change with ROIC?
36
36 Q as a function of ROIC ROIC Q
37
37 Let’s Try It Min Order Quantities!
38
38 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
39
39 In China: Solving for Q Last item: –Reward: (Revenue – Cost – ROIC*c i )*Prob. Demand exceeds Q –Risk: (Cost + ROIC*c i – Salvage) * Prob. Demand falls below Q –As though Cost increased by ROIC*c i Balance the two –(Revenue – Cost – ROIC*c i )*(1-P) = (Cost + ROIC*c i – Salvage)*P So P = (Profit – ROIC*c i )/(Revenue - Salvage) = Profit/(Revenue - Salvage) – ROIC*c i /(Revenue - Salvage) In our case –(Revenue - Salvage) = 32% Revenue, –Profit = 31.25% Revenue –c i = 68.75% Revenue So P = 31.25/32 – ROIC*68.75%/32% = 0.977 – 2.148*ROIC Recall that P is…. How does the order quantity Q change with ROIC?
40
40 And China? Min Order Quantities! 38.73% vs 25.5%
41
41 And Minimum Order Quantities Maximize Expected Profit(Q i ) – ROIC* c i Q i M*z i Q i 600*z i (M is a “big” number) z i binary (do we order this or not) If z i =1 we order at least 600 If z i =0 we order 0
42
42 Solving for Q’s L i (ROIC) = Maximize Expected Profit(Q i ) – ROIC*c i Q i s.t. M*z i Q i 600*z i z i binary Two answers to consider: z i = 0 then L i (ROIC) = 0 z i = 1 then Q i is easy to calculate It is just the larger of 600 and the Q that gives P = (Profit – ROIC*c i )/(Revenue - Salvage) (call it Q*) Which is larger Expected Profit(Q*) – ROIC*c i Q* or 0?
43
43 Which is Larger? What is the largest value of ROIC for which, Expected Profit(Q*) – ROIC*c i Q* > 0? Expected Profit(Q*)/c i Q* > ROIC Expected Return on Investment if we make Q* is at least this ROIC What is this bound? The return at the minimum order quantity!
44
44 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
45
45 Solving for Q’s L i (ROIC) = Maximize Expected Profit(Q i ) - ROIC*c i Q i s.t. M*z i Q i 600*z i z i binary Let’s first look at the problem with z i = 1 L i (ROIC) = Maximize Expected Profit(Q i ) - ROIC*c i Q i s.t. Q i 600 How does Q i change with ROIC?
46
46 Adding a Lower Bound ROIC Q
47
47 Solving for z i L i (ROIC) = Maximize Expected Profit(Q i ) - ROIC*c i Q i s.t. M*z i Q i 600*z i z i binary If z i is 0, the objective is 0 If z i is 1, the objective is Expected Profit(Q i ) – ROIC*c i Q i So, if Expected Profit(Q i ) – ROIC*c i Q i > 0, z i is 1 As we increase the ROIC, Q decreases. Once Q reaches its lower bound, L i (ROIC) decreases, When L i (ROIC) reaches 0, z i changes to 0 and remains 0 L i (ROIC) reaches 0 when ROIC is the return on 600 units.
48
48 Solving for z i That was a complicated way of saying that as Q increases, the ROIC decreases The highest ROIC a product can achieve is the ROIC at its minimum order quantity If the required ROIC goes above this, don’t make the product So, compute the ROIC at the minimum order quantity and use this to determine when to stop making the product
49
49 Answers China Hong Kong If everything is made in one place, where would you make it?
50
50 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) –Want to ensure a high return on invested capital
51
51 Different View Maximize Expected Profit(Q i ) S.t. c i Q i = Invested Capital Target That maximizes the ROIC for the “portfolio” How to do it?
52
52 Different View Use Lagrange Maximize Expected Profit(Q i ) - Tax Rate* c i Q i At a given Tax Rate, the answer maximizes the ROIC over all portfolios with that amount of Invested Capital. Increasing the Tax Rate reduces the Invested Capital So, we can carve out the frontier of high ROIC portfolios vs Invested Capital
53
53 Different View So What? There’s no constraint on Invested Capital There is a target for total units – 10,000 Adjust the Tax Rate until we find a high ROIC portfolio with close to 10,000 units
54
54 Summary Impose minimums (no choice of where to make them) –If the tax rate exceeds the ROIC 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
55
55 Where to Produce? If a style is not attractive to produce in China, it might be attractive in HK at the lower MOQ… 1 if We don’t make the product in China and is < Return at 600
56
56 Idea It’s attractive to make it in Hong Kong if –The return on 1,200 in China is lower than the tax rate (we don’t want to make it there) –but the 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. We always get a higher return on 1,200 in China than on 600 in HK –In fact the lowest return on 1200 in China is greater than the highest return on 600 in HK. Conclusion: Only use HK after the Vegas show for small volume products.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.