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

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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 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!

8

The Critical Path of the SC

- Contract for Greige
- Production Plans set
- Dying and printing
- YKK Zippers

10

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?

11

Production Planning Example

- Rococo Parka
- Wholesale price $112.50
- Average profit 24%*112.50 = $27
- Average loss 8%*112.50 = $9

12

Recall the Newsvendor

- Ignoring all other constraints recommended target stock out probability is:
1-Profit/(Profit + Risk)

=8%/(24%+8%) = 25%

14

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

15

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

17

First Order Objective

Expected Profit

Invested Capital

- Maximize t =
- Can we exceed return t*?
- Is
L(t*) = Max Expected Profit - t*Invested Capital > 0?

18

First Order Objective

- Initially Ignore the prices we pay
- Treat every unit as though it costs Sport Obermeyer $1
- Maximize l =
- Can we achieve return l?
- L(l) = Max Expected Profit - lS Qi > 0?

Expected Profit

Number of Units Produced

19

Solving for Qi

- For l fixed, how to solve
L(l) = Maximize S Expected Profit(Qi) - lS Qi

s.t. Qi 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
- l?

- Set P = (Profit – l)/(Profit + Risk)
= 0.75 –l/(Profit + Risk)

Error here: let p be the wholesale price,

Profit = 0.24*p

Risk = 0.08*p

P = (0.24p – l)/(0.24p + 0.08p)

= 0.75 - l/(.32p)

20

Solving for Qi

- Last item:
- Profit: Profit*Probability Demand exceeds Q
- Risk:Risk * Probability Demand falls below Q
- Also pay l for each item

- Balance the two sides:
Profit*(1-P) – l = Risk*P

Profit – l = (Profit + Risk)*P

- So P = (Profit – l)/(Profit + Risk)
- In our case Profit = 24%, Risk = 8% so
P = .75 – l/(.32*Wholesale Price)

How does the order quantity Q change with l?

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.

21

Q as a function of l

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.

Q

l

22

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

23

And Minimum Order Quantities

Maximize S Expected Profit(Qi) - lSQi

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

24

Solving for Q’s

Li(l) = Maximize Expected Profit(Qi) - lQi

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 - l)/(profit + risk) (call it Q*)

Which is larger Expected Profit(Q*) – lQ* or 0?

Find the largest l for which this is positive. For

l greater than this, Q is 0.

25

Solving for Q’s

Li(l) = Maximize Expected Profit(Qi) - lQi

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) - lQi

s.t. Qi 600

How does Qi change with l?

26

Objective Function

- How does Objective Function change with l?
Li(l) = Maximize Expected Profit(Qi) – lQi

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

28

Solving for zi

Li(l) = Maximize Expected Profit(Qi) - lQi

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) - lQi

So, if Expected Profit(Qi) – lQi > 0, zi is 1

Once Q reaches its lower bound, Li(l) decreases, when it reaches 0, zi changes to 0 and remains 0

30

Answers

Error: That resolves the question of why we got a higher return in China with no cost differences!

Hong Kong

China

31

First Order Objective: With Prices

- It makes sense that l, 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.

32

First Order Objective: With Prices

Expected Profit

S ciQi

- Maximize l =
- Can we achieve return l?
- L(l) = Max Expected Profit - lSciQi > 0?
- What goes into ci ?
- Consider Rococo example
- Cost 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

33

Gail

Make it in China

Expected Profit above Target Rate of Return

Make it in Hong Kong

Stop Making It.

Target Rate of Return

35

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.

36

Where to Make What?

That little cleverness was worth 2%

Not a big deal. Make Gail in HK at minimum

37

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.

38

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