11

Sport Obermeyer Case

John H. Vande Vate

Spring, 2006

22

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

33

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

44

Production Options

• Hong Kong– More expensive– Smaller lot sizes– Faster– More flexible

• Mainland (Guangdong, Lo Village)

– Cheaper– Larger lot sizes– Slower– Less flexible

55

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)

66

The Product

• Gender– Styles– Colors– Sizes

• Total Number of SKU’s: ~800

77

Service

• Deliver matching collections simultaneously

• Deliver early in the season

88

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!

99

Quotas

• Force delivery earlier in the season

• Last man loses.

1010

The Critical Path of the SC

• Contract for Greige

• Production Plans set

• Dying and printing

• YKK Zippers

1111

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?

1212

Production Planning Example

• Rococo Parka

• Wholesale price $112.50

• Average profit 24%*112.50 = $27

• Average loss 8%*112.50 = $9

1313

Sample ProblemStyle Price Laura Carolyn Greg Wendy Tom Wally Average Std. Dev 2X Std DevGail 110.00$ 900 1,000 900 1,300 800 1,200 1,017 194 388 Isis 99.00$ 800 700 1,000 1,600 950 1,200 1,042 323 646 Entice 80.00$ 1,200 1,600 1,500 1,550 950 1,350 1,358 248 496 Assault 90.00$ 2,500 1,900 2,700 2,450 2,800 2,800 2,525 340 680 Teri 123.00$ 800 900 1,000 1,100 950 1,850 1,100 381 762 Electra 173.00$ 2,500 1,900 1,900 2,800 1,800 2,000 2,150 404 807 Stephanie 133.00$ 600 900 1,000 1,100 950 2,125 1,113 524 1,048 Seduced 73.00$ 4,600 4,300 3,900 4,000 4,300 3,000 4,017 556 1,113 Anita 93.00$ 4,400 3,300 3,500 1,500 4,200 2,875 3,296 1047 2,094 Daphne 148.00$ 1,700 3,500 2,600 2,600 2,300 1,600 2,383 697 1,394 Total 20,000 20,000 20,000 20,000 20,000 20,000 20,000

Cut and Sew Capacity3000 Units/month

7 month period

First Phase Commitment10,000 units

Second Phase Commitment10,000 units

Individual Forecasts

1414

Recall the Newsvendor

• Ignoring all other constraints recommended target stock out probability is:

1-Profit/(Profit + Risk)

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

1515

Ignoring ConstraintsStyle Mean Std Dev Recommended Order QuantityGail 1,017 388 1,278 Isis 1,042 646 1,478 Entice 1,358 496 1,693 Assault 2,525 680 2,984 Teri 1,100 762 1,614 Electra 2,150 807 2,695 Stephanie 1,113 1048 1,819 Seduced 4,017 1113 4,767 Anita 3,296 2094 4,708 Daphne 2,383 1394 3,323

26,359 Note This suggests over buying!

Everyone has a 25% chance of stockoutEveryone orders Mean + 0.6745

P = .75 [from .24/(.24+.08)]Probability of being less thanMean + 0.6745 is 0.75

1616

Constraints

• Make at least 10,000 units in initial phase

• Minimum Order Quantities

1717

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

1818

First Order Objective

• Maximize =

• Can we exceed return *?

• Is

L(*) = Max Expected Profit - *Invested Capital > 0?

Expected Profit

Invested Capital

1919

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 - Qi > 0?

Expected Profit

Number of Units Produced

2020

Solving for Qi

• For fixed, how to solve

L() = Maximize Expected Profit(Qi) - 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–

• Set P = (Profit – )/(Profit + Risk) = 0.75 –/(Profit + Risk)

Error here: let p be the wholesale price, Profit = 0.24*pRisk = 0.08*pP = (0.24p – )/(0.24p + 0.08p) = 0.75 - /(.32p)

2121

Solving for Qi

• 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.

2222

0

200

400

600

800

1000

1200

1400

-3 2 7 12 17 22 27

Q as a function of

Q

Doh! As we demand a higher return, we can acceptless and less risk that the item won’t sell. So,

We make less and less.

2323

Let’s Try ItStyle Mean Std Dev Recommended Order Quantity

Wholesale Price Order Quantity at Return

Gail 1,017 388 1,278 110.00$ 749 1778.1474%Isis 1,042 646 1,478 99.00$ 471Entice 1,358 496 1,693 80.00$ 568Assault 2,525 680 2,984 90.00$ 1767Teri 1,100 762 1,614 123.00$ 697Electra 2,150 807 2,695 173.00$ 2005Stephanie 1,113 1048 1,819 133.00$ 658Seduced 4,017 1113 4,767 73.00$ 0Anita 3,296 2094 4,708 93.00$ 1148Daphne 2,383 1394 3,323 148.00$ 1938

26,359 10,000

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

2424

And Minimum Order Quantities

Maximize Expected Profit(Qi) - Qi

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

2525

Solving for Q’s

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

s.t. M*zi Qi 600*zi

zi binaryTwo answers to consider:

zi = 0 then Li() = 0

zi = 1 then Qi is easy to calculateIt 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. Forgreater than this, Q is 0.

2626

Solving for Q’s

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

s.t. M*zi Qi 600*zi

zi binary

Let’s first look at the problem with zi = 1

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

s.t. Qi 600

How does Qi change with ?

2727

Adding a Lower Bound

Q

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

2828

Objective Function

• How does Objective Function change with ?

Li() = Maximize Expected Profit(Qi) – Qi

We know Expected Profit(Qi) is concave

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

- 500 1,000 1,500 2,000 2,500 3,000 3,500

As increases, Q decreases

and so does the Expected Profit

When Q hits its lower bound, it remains there.

After that Li() decreases linearly

2929

The Relationships

-$50

$0

$50

$100

$150

$200

$250

0 0.05 0.1 0.15 0.2 0.25

Expected Profit

Capital Charge

L(lambda)

Q reaches minimum

Capital Charge = Expected Profit

Past here, Q = 0

3030

Solving for zi

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

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) - Qi

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

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

3131

Style Mean Std Dev

Recommended Order

QuantityWholesale

Price Lagrange Order Quantity

Min Order

Quantity

Max Order

Quantity Order?Lambda Limit

at 1200Lambda

limit at 600

Gail 1,017 388 1,278 110.00$ 717 1864.10% 600 1,278 1 1869% 2478%Isis 1,042 646 1,478 99.00$ 600 600 1,478 1 1505% 1952%Entice 1,358 496 1,693 80.00$ 600 600 1,693 1 1647% 1864%Assault 2,525 680 2,984 90.00$ 1664 600 2,984 1 2160% 2160%Teri 1,100 762 1,614 123.00$ 648 600 1,614 1 1866% 2350%Electra 2,150 807 2,695 173.00$ 1973 600 2,695 1 3937% 4083%Stephanie 1,113 1048 1,819 133.00$ 600 600 1,819 1 1824% 2247%Seduced 4,017 1113 4,767 73.00$ 600 600 4,767 1 1752% 2634%Anita 3,296 2094 4,708 93.00$ 873 600 4,708 1 1928% 2003%Daphne 2,383 1394 3,323 148.00$ 1870 600 3,323 1 3044% 3225%

26,359 10,145

Answers

China

Hong Kong

In China?

Style Mean Std Dev

Recommended Order

QuantityWholesale

Price Lagrange Order Quantity

Min Order

Quantity

Max Order

Quantity Order?Lambda Limit

at 1200Lambda

limit at 600

Gail 1,017 388 1,278 110.00$ 1200 1824.04% 1200 1,278 1 1869% 2478%Isis 1,042 646 1,478 99.00$ 0 0 - 0 1505% 1952%Entice 1,358 496 1,693 80.00$ 0 0 - 0 1647% 1864%Assault 2,525 680 2,984 90.00$ 1714 1200 2,984 1 2160% 2160%Teri 1,100 762 1,614 123.00$ 1200 1200 1,614 1 1866% 2350%Electra 2,150 807 2,695 173.00$ 1988 1200 2,695 1 3937% 4083%Stephanie 1,113 1048 1,819 133.00$ 1200 1200 1,819 1 1824% 2247%Seduced 4,017 1113 4,767 73.00$ 0 0 - 0 1752% 1752%Anita 3,296 2094 4,708 93.00$ 1200 1200 4,708 1 1928% 2003%Daphne 2,383 1394 3,323 148.00$ 1902 1200 3,323 1 3044% 3225%

26,359 10,404

Error: That resolves the question of why we got a higher return in

China with no cost differences!

3232

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.

3333

First Order Objective: With Prices

• Maximize =

• Can we achieve return ?

• L() = Max Expected Profit - ciQi > 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

Expected Profit

ciQi

3434

Return on Capital

Hong KongStyle Mean Std Dev

Recommended Order

QuantityWholesale

Price Lagrange Order Quantity

Min Order

Quantity

Max Order

Quantity Order?Lambda Limit

at 1200Lambda

limit at 600

Gail 1,017 388 1,278 110.00$ 608 36.19% 600 1,278 1 31.8% 42.2%Isis 1,042 646 1,478 99.00$ 600 600 1,478 1 28.5% 36.9%Entice 1,358 496 1,693 80.00$ 836 600 1,693 1 38.5% 43.6%Assault 2,525 680 2,984 90.00$ 1808 600 2,984 1 44.9% 44.9%Teri 1,100 762 1,614 123.00$ 0 0 - 0 28.4% 35.8%Electra 2,150 807 2,695 173.00$ 1299 600 2,695 1 42.6% 44.2%Stephanie 1,113 1048 1,819 133.00$ 0 0 - 0 25.7% 31.6%Seduced 4,017 1113 4,767 73.00$ 2844 600 4,767 1 44.9% 44.9%Anita 3,296 2094 4,708 93.00$ 1090 600 4,708 1 38.8% 40.3%Daphne 2,383 1394 3,323 148.00$ 915 600 3,323 1 38.5% 40.8%

26,359 10,000

Style Mean Std Dev

Recommended Order

QuantityWholesale

Price Lagrange Order Quantity

Min Order

Quantity

Max Order

Quantity Order?Lambda Limit

at 1200Lambda

limit at 600

Gail 1,017 388 1,278 110.00$ 0 39.87% 0 - 0 36.8% 48.8%Isis 1,042 646 1,478 99.00$ 0 0 - 0 32.9% 42.7%Entice 1,358 496 1,693 80.00$ 1200 1200 1,693 1 44.6% 50.5%Assault 2,525 680 2,984 90.00$ 1889 1200 2,984 1 52.0% 52.0%Teri 1,100 762 1,614 123.00$ 0 0 - 0 32.9% 41.4%Electra 2,150 807 2,695 173.00$ 1395 1200 2,695 1 49.3% 51.1%Stephanie 1,113 1048 1,819 133.00$ 0 0 - 0 29.7% 36.6%Seduced 4,017 1113 4,767 73.00$ 2976 1200 4,767 1 52.0% 52.0%Anita 3,296 2094 4,708 93.00$ 1339 1200 4,708 1 44.9% 46.7%Daphne 2,383 1394 3,323 148.00$ 1200 1200 3,323 1 44.6% 47.2%

26,359 10,000

China

If everything is made in one place, where would you

make it?

3535

Gail

-$10,000

-$5,000

$0

$5,000

$10,000

$15,000

$20,000

$25,000

0% 10% 20% 30% 40% 50%

Hong Kong

China

Expected Profit above Target Rate of Return

Target Rate of Return

Make it in China

Make it in Hong Kong

Stop Making It.

3636

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.

3737

Style Mean Std DevRecommended Order Quantity

Wholesale Price

Order Quantity

Using Lambda

Min Order

Quantity

Max Order

Quantity Order Lambda Limit

Gail 1,017 388 1,278 110.00$ 0 42.19% 0 - 0 26.9%Isis 1,042 646 1,478 99.00$ 0 0 - 0 27.1%Entice 1,358 496 1,693 80.00$ 1200 1200 1,693 1 44.6%Assault 2,525 680 2,984 90.00$ 1794 1200 2,984 1 52.0%Teri 1,100 762 1,614 123.00$ 0 0 - 0 28.8%Electra 2,150 807 2,695 173.00$ 1283 1200 2,695 1 49.3%Stephanie 1,113 1048 1,819 133.00$ 0 0 - 0 27.1%Seduced 4,017 1113 4,767 73.00$ 2822 1200 4,767 1 52.0%Anita 3,296 2094 4,708 93.00$ 1200 1200 4,708 1 44.9%Daphne 2,383 1394 3,323 148.00$ 1200 1200 3,323 1 44.6%

Gail 1,017 388 1,278 110.00$ 600 600 1,278 1 42.2%Isis 1,042 646 1,478 99.00$ 0 0 - 0 36.9%Entice 1,358 496 1,693 80.00$ 0 0 - 0 43.6%Assault 2,525 680 2,984 90.00$ 0 0 - 0 44.9%Teri 1,100 762 1,614 123.00$ 0 0 - 0 35.8%Electra 2,150 807 2,695 173.00$ 0 0 - 0 44.2%Stephanie 1,113 1048 1,819 133.00$ 0 0 - 0 31.6%Seduced 4,017 1113 4,767 73.00$ 0 0 - 0 44.9%Anita 3,296 2094 4,708 93.00$ 0 0 - 0 40.3%Daphne 2,383 1394 3,323 148.00$ 0 0 - 0 40.8%

10,099

Same Styles Made in Hong Kong

Where to Make What?That little cleverness

was worth 2%

Not a big deal. Make Gail in HK at

minimum

3838

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.