Sport Obermeyer Case
John H. Vande Vate
Spring, 2006
1
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
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
3
Production Options
• Hong Kong
–
–
–
–
• Mainland (Guangdong, Lo Village)
More expensive
Smaller lot sizes
Faster
More flexible
–
–
–
–
Cheaper
Larger lot sizes
Slower
Less flexible
4
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
5
The Product
• Gender
– Styles
– Colors
– Sizes
• Total Number of SKU’s: ~800
6
6
Service
• Deliver matching collections
simultaneously
• Deliver early in the season
7
7
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)
8
Replenishment orders from Retailers
Quotas!
8
Quotas
• Force delivery earlier in the season
• Last man loses.
9
9
The Critical Path of the SC
•
•
•
•
Contract for Greige
Production Plans set
Dying and printing
YKK Zippers
10
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
11
Production Planning Example
•
•
•
•
Rococo Parka
Wholesale price $112.50
Average profit 24%*112.50 = $27
Average loss 8%*112.50 = $9
12
12
Sample Problem
Style
Price
Laura
Carolyn
Gail
$ 110.00
900
1,000
Isis
$ 99.00
800
700
Entice
$ 80.00
1,200
1,600
Assault
$ 90.00
2,500
1,900
Teri
$ 123.00
800
900
Electra
$ 173.00
2,500
1,900
Stephanie $ 133.00
600
900
Seduced $ 73.00
4,600
4,300
Anita
$ 93.00
4,400
3,300
Daphne
$ 148.00
1,700
3,500
Total
20,000
20,000
Individual Forecasts
Greg
Wendy
Tom
Wally
Average
Std. Dev 2X Std Dev
900
1,300
800
1,200
1,017
194
388
1,000
1,600
950
1,200
1,042
323
646
1,500
1,550
950
1,350
1,358
248
496
2,700
2,450
2,800
2,800
2,525
340
680
1,000
1,100
950
1,850
1,100
381
762
1,900
2,800
1,800
2,000
2,150
404
807
1,000
1,100
950
2,125
1,113
524
1,048
3,900
4,000
4,300
3,000
4,017
556
1,113
3,500
1,500
4,200
2,875
3,296
1047
2,094
2,600
2,600
2,300
1,600
2,383
697
1,394
20,000
20,000
20,000
20,000
20,000
Cut and Sew Capacity
3000 Units/month
7 month period
First Phase Commitment
10,000 units
Second Phase Commitment
10,000 units
13
13
Recall the Newsvendor
• Ignoring all other constraints
recommended target stock out probability
is:
1-Profit/(Profit + Risk)
=8%/(24%+8%) = 25%
14
14
Ignoring Constraints
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
Std Dev Recommended Order Quantity
1,017
388
1,278
1,042
646
1,478
1,358
496
1,693
2,525
680
2,984
1,100
762
1,614
2,150
807
2,695
1,113
1048
1,819
4,017
1113
4,767
3,296
2094
4,708
2,383
1394
3,323
26,359 Note This suggests over buying!
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
15
Constraints
• Make at least 10,000 units in initial phase
• Minimum Order Quantities
16
16
Objective for the “first 10K”
• First Order criteria:
– Return on Investment:
Expected Profit
Invested Capital
• Second Order criteria:
– Standard Deviation in Return
• Worry about First Order first
17
17
First Order Objective
• Maximize t = Expected Profit
Invested Capital
• Can we exceed return t*?
• Is
L(t*) = Max Expected Profit - t*Invested Capital > 0?
18
18
First Order Objective
• Initially Ignore the prices we pay
• Treat every unit as though it costs Sport
Obermeyer $1
Expected
Profit
• Maximize l =
Number of Units Produced
• Can we achieve return l?
• L(l) = Max Expected Profit - lS Qi > 0?
19
19
Solving for Qi
• For l fixed, how to solve
L(l) = Maximize S Expected Profit(Qi) - l S Qi
Error here: let p be the
s.t. Qi  0
wholesale price,
Note it is separable (separate decision each Q)
Profit = •0.24*p
Risk = 0.08*p
• Exactly the same thinking!
P = (0.24p
l)/(0.24p
• –Last
item: + 0.08p)
= 0.75 - l/(.32p)
– 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)
20
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
Error: This was omitted. It is
not needed later when we
calculate cost as, for
53.4%*Wholesale
Profit*(1-P) – lexample,
=
Risk*P
price, because it factors out
of everything.
Profit – l = (Profit + Risk)*P
• Balance the two sides:
• 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?
21
21
Q as a function of l
1400
1200
Doh!
As we demand a higher return, we can accept
800
less and less risk that the item won’t sell. So,
600
We make less and less.
1000
Q
400
200
0
-3
2
7
12
l
17
22
27
22
22
Let’s Try It
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
Std Dev
1,017
388
1,042
646
1,358
496
2,525
680
1,100
762
2,150
807
1,113
1048
4,017
1113
3,296
2094
2,383
1394
Wholesale
Price
Recommended
Order Quantity
1,278 $ 110.00
1,478 $
99.00
1,693 $
80.00
2,984 $
90.00
1,614 $ 123.00
2,695 $ 173.00
1,819 $ 133.00
4,767 $
73.00
4,708 $
93.00
3,323 $ 148.00
26,359
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
Order Quantity at Return
l
749 1778.1474%
471
568
1767
697
2005
658
0
1148
1938
10,000
Min Order
Quantities!
23
23
And Minimum Order Quantities
Maximize S Expected Profit(Qi) - l SQi
M*zi  Qi  600*zi (M is a “big” number)
zi binary
(do we order this or not)
If zi =0 we
order 0
If zi =1 we
order at
least 600
24
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
25
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
26
Adding a Lower Bound
1400
1200
1000
800
Q
600
400
200
0
0
5
10
15
20
25
l
27
27
Objective Function
•
How does Objective Function change
with l?
Li(l) = Maximize Expected Profit(Qi) – lQi
We know Expected Profit(Qi) is concave
$30,000
As l increases,
Q decreases
and so does the
Expected Profit
$25,000
$20,000
$15,000
$10,000
When Q hits its
lower bound, it
remains there.
After that Li(l)
decreases linearly
$5,000
28
$0
28
The Relationships
$250
Expected Profit
Capital Charge
$200
L(lambda)
Capital Charge =
Expected Profit
$150
$100
Q reaches
minimum
$50
Past here, Q = 0
$0
0
0.05
0.1
0.15
0.2
0.25
-$50
l/110
29
29
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
30
Answers
Hong Kong
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Recomm
ended
Min
Order Wholesale
Order
Price
Quantity
Std Dev Quantity
Lagrange Order Quantity
l
388
1,278 $ 110.00
717 1864.10%
600
646
1,478 $
99.00
600
600
496
1,693 $
80.00
600
600
680
2,984 $
90.00
1664
600
762
1,614 $ 123.00
648
600
807
2,695 $ 173.00
1973
600
1048
1,819 $ 133.00
600
600
1113
4,767 $
73.00
600
600
2094
4,708 $
93.00
873
600
1394
3,323 $ 148.00
1870
600
26,359
10,145
In
China?
Error: That resolves
the question of why we
got a higher return in
China with no cost
differences!
Max
Order
Quantity
Lambda Limit
Lambda
at 1200
limit at 6
Order?
1,278
1,478
1,693
2,984
1,614
2,695
1,819
4,767
4,708
3,323
1
1
1
1
1
1
1
1
1
1
1869%
1505%
1647%
2160%
1866%
3937%
1824%
1752%
1928%
3044%
247
195
186
216
235
408
224
263
200
322
China
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Recomm
ended
Min
Order Wholesale
Order
Price
Quantity
Std Dev Quantity
Lagrange Order Quantity
l
388
1,278 $ 110.00
1200 1824.04%
1200
646
1,478 $
99.00
0
0
496
1,693 $
80.00
0
0
680
2,984 $
90.00
1714
1200
762
1,614 $ 123.00
1200
1200
807
2,695 $ 173.00
1988
1200
1048
1,819 $ 133.00
1200
1200
1113
4,767 $
73.00
0
0
2094
4,708 $
93.00
1200
1200
1394
3,323 $ 148.00
1902
1200
26,359
10,404
Max
Order
Quantity
1,278
2,984
1,614
2,695
1,819
4,708
3,323
Lambda Limit
at 1200
Order?
1
0
0
1
1
1
1
0
1
1
1869%
1505%
1647%
2160%
1866%
3937%
1824%
1752%
1928%
3044%
31
Lambda
limit at 600
2478%
1952%
1864%
2160%
2350%
4083%
2247%
1752%
2003%
3225%
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
32
First Order Objective:
With Prices
• Maximize l =
•
•
•
•
•
Expected Profit
S ciQi
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
33
Return on Capital
If everything isHong Kong
made in one place,
where would you
make it?
China
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Mean
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Recomm
ended
Order Wholesale
Price
Std Dev Quantity
Lagrange Order Quantity
388
1,278 $ 110.00
608
646
1,478 $
99.00
600
496
1,693 $
80.00
836
680
2,984 $
90.00
1808
762
1,614 $ 123.00
0
807
2,695 $ 173.00
1299
1048
1,819 $ 133.00
0
1113
4,767 $
73.00
2844
2094
4,708 $
93.00
1090
1394
3,323 $ 148.00
915
26,359
10,000
Recomm
ended
Order Wholesale
Price
Std Dev Quantity
Lagrange Order Quantity
388
1,278 $ 110.00
0
646
1,478 $
99.00
0
496
1,693 $
80.00
1200
680
2,984 $
90.00
1889
762
1,614 $ 123.00
0
807
2,695 $ 173.00
1395
1048
1,819 $ 133.00
0
1113
4,767 $
73.00
2976
2094
4,708 $
93.00
1339
1394
3,323 $ 148.00
1200
26,359
10,000
l
36.19%
l
39.87%
Min
Order
Quantity
Max
Order
Quantity
600
600
600
600
0
600
0
600
600
600
1,278
1,478
1,693
2,984
2,695
4,767
4,708
3,323
Min
Order
Quantity
Max
Order
Quantity
0
0
1200
1200
0
1200
0
1200
1200
1200
1,693
2,984
2,695
4,767
4,708
3,323
Lambda Limit
Lambda
at 1200
limit at 600
Order?
1
1
1
1
0
1
0
1
1
1
31.8%
28.5%
38.5%
44.9%
28.4%
42.6%
25.7%
44.9%
38.8%
38.5%
42.2%
36.9%
43.6%
44.9%
35.8%
44.2%
31.6%
44.9%
40.3%
40.8%
Lambda Limit
Lambda
at 1200
limit at 600
Order?
0
0
1
1
0
1
0
1
1
1
36.8%
32.9%
44.6%
52.0%
32.9%
49.3%
29.7%
52.0%
34
44.9%
44.6%
48.8%
42.7%
50.5%
52.0%
41.4%
51.1%
36.6%
52.0%
46.7%
47.2%
34
Gail
Make it in
Hong Kong
China
China
Make it in
Hong Kong
$25,000
$20,000
Expected
Profit
above
Target
Rate of
Return
$15,000
$10,000
$5,000
$0
0%
-$5,000
-$10,000
10%
20%
30%
40%
50%
Stop
Making It.
Target Rate of Return
35
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
36
That
little
Where to Make What?
cleverness
was worth 2%
Style
Mean
Gail
1,017
Isis
1,042
Entice
1,358
Assault
2,525
Teri
1,100
Electra
2,150
Stephanie
1,113
Seduced
4,017
Anita
3,296
Daphne
2,383
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Recommended
Std Dev Order Quantity
388
1,278
646
1,478
496
1,693
680
2,984
762
1,614
807
2,695
1048
1,819
1113
4,767
2094
4,708
1394
3,323
388
646
496
680
762
807
1048
1113
2094
1394
1,278
1,478
1,693
2,984
1,614
2,695
1,819
4,767
4,708
3,323
Wholesale
Price
$
$
$
$
$
$
$
$
$
$
110.00
99.00
80.00
90.00
123.00
173.00
133.00
73.00
93.00
148.00
$
$
$
$
$
$
$
$
$
$
110.00
99.00
80.00
90.00
123.00
173.00
133.00
73.00
93.00
148.00
Order
Quantity
Using
Lambda
l
Min
Order
Quantity
0
42.19%
0
0
0
1200
1200
1794
1200
0
0
1283
1200
0
0
2822
1200
1200
1200
1200
1200
Same Styles Made in Hong Kong
600
600
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10,099
Max
Order
Quantity
1,693
2,984
2,695
4,767
4,708
3,323
Order
0
0
1
1
0
1
0
1
1
1
Lambda Limit
26.9%
27.1%
44.6%
52.0%
28.8%
49.3%
27.1%
52.0%
44.9%
44.6%
1,278
-
1
0
0
0
0
0
0
0
0
0
42.2%
36.9%
43.6%
44.9%
35.8%
44.2%
31.6%
44.9%
40.3%
40.8%
Not a big deal. Make
Gail in HK at
minimum
37
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
38