Sport Obermeyer Case John H. Vande Vate Spring, 2007 1
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
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
Production Options • Hong Kong • More expensive • Smaller lot sizes • Faster • More flexible • Mainland (Guangdong, Lo Village) • Cheaper • Larger lot sizes • Slower • Less flexible 4
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
The Product • Gender • Styles • Colors • Sizes • Total Number of SKU’s: ~800 6
Service • Deliver matching collections simultaneously • Deliver early in the season 7
Production Planning Example • Rococo Parka • Wholesale price $112.50 • Average profit 24%*112.50 = $27 • Average loss 8%*112.50 = $9 8
Sample Problem 9
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
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
Getting a Distribution • Generate a point estimate via usual process • Apply the historical distribution of A/F ratios to this point forecast. 12
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
Question • Expected impact • P = Probability Demand < Q • Reward: (Selling Price – Cost)*(1-P) • Risk: (Cost – Salvage)*P • How much to order? 14
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
For Obermeyer • Ignoring all other constraints recommended target stock out probability is: = 8%/(24%+8%) = 25% 16
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
Constraints • Make at least 10,000 units in initial phase • Minimum Order Quantities 18
Objective for the “first 10K” • Return on Investment: Expected Profit Invested Capital 19
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
First Phase Objective: Expected Profit S ciQi • Maximize l = • Can we achieve return l? • L(l) = Max Expected Profit - lSciQi > 0? 21
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
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
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
Q as a function of l Q l 25
Let’s Try It Min Order Quantities! 26
57% vs 36% And China? Min Order Quantities! 27
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
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
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
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
Adding a Lower Bound Q l 32
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
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
Answers Hong Kong If everything is made in one place, where would you make it? China 35
Where to Produce? 36
Other issues? • Aggressive view of Risk: Maximum Return • Other issues not addressed? • Other measures of risk? 37
