1 1 Sport Obermeyer Case John H. Vande Vate Spring, 2006

2 2 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

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 –More expensive –Smaller lot sizes –Faster –More flexible Mainland (Guangdong, Lo Village) –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 The Process –Design (February ’92) –Prototypes (July ’92) –Final Designs (September ’92) –Sample Production, Fabric & Component orders (50%) –Cut & Sew begins (February, ’93) –Las Vegas show (March, ’93 80% of orders) –SO places final orders with OL –OL places orders for components –Alpine & Subcons Cut & Sew –Transport to Seattle (June – July) –Retailers want full delivery prior to start of season (early September ‘93) –Replenishment orders from Retailers Quotas!

9 9 Quotas Force delivery earlier in the season Last man loses.

10 The Critical Path of the SC Contract for Greige Production Plans set Dying and printing YKK Zippers

11 Driving 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 How are these questions related?

12 Production Planning Example Rococo Parka Wholesale price $ Average profit 24%* = $27 Average loss 8%* = $9

13 Sample Problem

14 Recall the Newsvendor Ignoring all other constraints recommended target stock out probability is: 1-Profit/(Profit + Risk) =8% / (24%+8%) = 25%

15 Ignoring Constraints Everyone has a 25% chance of stockout Everyone orders Mean  P =.75 [from.24/( )] Probability of being less than Mean  is 0.75

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

17 Objective for the “first 10K” First Order criteria: –Return on Investment: Second Order criteria: –Standard Deviation in Return Worry about First Order first Expected Profit Invested Capital

18 First Order Objective Maximize  = Can we exceed return  *? Is L(  *) = Max Expected Profit -  *Invested Capital > 0? Expected Profit Invested Capital

19 First Order Objective Initially Ignore the prices we pay Treat every unit as though it costs Sport Obermeyer $1 Maximize = Can we achieve return ? L( ) = Max Expected Profit -  Q i > 0? Expected Profit Number of Units Produced

20 Solving for Q i For fixed, how to solve L( ) = Maximize  Expected Profit(Q i ) -  Q i s.t. Q i  0 Note it is separable (separate decision each Q) Exactly the same thinking! Last item: –Profit: Profit*Probability Demand exceeds Q –Risk: Loss * Probability Demand falls below Q –  Set P = (Profit – )/(Profit + Risk) = 0.75 – /(Profit + Risk) Error here: let p be the wholesale price, Profit = 0.24*p Risk = 0.08*p P = (0.24p – )/(0.24p p) = /(.32p)

21 Solving for Q i Last item: –Profit: Profit*Probability Demand exceeds Q –Risk:Risk * Probability Demand falls below Q – Also pay  for each item Balance the two sides: Profit*(1-P) – = Risk*P Profit – = (Profit + Risk)*P So P = (Profit – )/(Profit + Risk) In our case Profit = 24%, Risk = 8% so P =.75 – /(.32*Wholesale Price) How does the order quantity Q change with ? Error: This was omitted. It is not needed later when we calculate cost as, for example, 53.4%*Wholesale price, because it factors out of everything.

22 Q as a function of Q Doh! As we demand a higher return, we can accept less and less risk that the item won’t sell. So, We make less and less.

23 Let’s Try It Min Order Quantities! Adding the Wholesale price brings returns in line with expectations: if we can make $26.40 = 24% of $110 on a $1 investment, that’s a 2640% return

24 And Minimum Order Quantities Maximize  Expected Profit(Q 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

25 Solving for Q’s L i ( ) = Maximize Expected Profit(Q 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 ( ) = 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 - )/(profit + risk) (call it Q*) Which is larger Expected Profit(Q*) – Q* or 0? Find the largest  for which this is positive. For  greater than this, Q is 0.

26 Solving for Q’s L i ( ) = Maximize Expected Profit(Q 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 ( ) = Maximize Expected Profit(Q i ) - Q i s.t. Q i  600 How does Q i change with ?

27 Adding a Lower Bound Q

28 Objective Function How does Objective Function change with ? L i ( ) = Maximize Expected Profit(Q i ) – Q i We know Expected Profit(Q i ) is concave As increases, Q decreases and so does the Expected Profit When Q hits its lower bound, it remains there. After that L i ( ) decreases linearly

29 The Relationships  Q reaches minimum Capital Charge = Expected Profit Past here, Q = 0

30 Solving for z i L i ( ) = Maximize Expected Profit(Q 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 ) - Q i So, if Expected Profit(Q i ) – Q i > 0, z i is 1 Once Q reaches its lower bound, L i ( ) decreases, when it reaches 0, z i changes to 0 and remains 0

31 Answers China Hong Kong In China? Error: That resolves the question of why we got a higher return in China with no cost differences!

32 First Order Objective: With Prices It makes sense that  the desired rate of return on capital at risk, should get very high, e.g., 1240%, before we would drop a product completely. The $1 investment per unit we used is ridiculously low. For Seduced, that $1 promises 24%*$73 = $17.52 in profit (if it sells). That would be a 1752% return! Let’s use more realistic cost information.

33 First Order Objective: With Prices Maximize = Can we achieve return ? L( ) = Max Expected Profit -  c i Q i > 0? What goes into c i ? Consider Rococo example Cost is $60.08 on Wholesale Price of $ or 53.4% of Wholesale Price. For simplicity, let’s assume c i = 53.4% of Wholesale Price for everything from HK and 46.15% from PRC Expected Profit  c i Q i

34 Return on Capital Hong Kong China If everything is made in one place, where would you make it?

35 Gail Expected Profit above Target Rate of Return Target Rate of Return Make it in China Make it in Hong Kong Stop Making It.

36 What Conclusions? There is a point beyond which the smaller minimum quantities in Hong Kong yield a higher return even though the unit cost is higher. This is because we don’t have to pay for larger quantities required in China and those extra units are less likely to sell. Calculate the “return of indifference” (when there is one) style by style. Only produce in Hong Kong beyond this limit.

37 Where to Make What? That little cleverness was worth 2% Not a big deal. Make Gail in HK at minimum

38 What Else? Kai’s point about making an amount now that leaves less than the minimum order quantity for later Secondary measure of risk, e.g., the variance or std deviation in Profit.