Sport Obermeyer
What to order?
What are the issues?
A Sample Problem
Commit 10,000 units before show
Commit 10,000 units after show
Minimum of 600 units
A First Approach
Ignore differences in
Profit margins
Salvage values
Ignore minimum lot sizes
Consider only first order cycle
Sample Problem
Style
Mean Forecast Std Deviation in Demand
Gail
1,017
388
Isis
1,042
646
Entice
1,358
496
Assault
2,525
680
Teri
1,100
762
Electra
2,150
807
Stephanie
1,113
1,048
Seduced
4,017
1,113
Anita
3,296
2,094
Daphne
2,383
1,394
Normal Distribution
0.45
0.4
0.35
0.3
0.25
0.2
0.15
Std Dev.s
0.1
0.05
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
Idea 1
Make all products equally likely to sell out
Choose a single std dev. To set production
quotas for all products
What should the Std. Dev. Be?
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
Forecast
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Std Deviation in
Demand
388
646
496
680
762
807
1,048
1,113
2,094
1,394
Total Production
Order
Amount
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
20,001
Std. Devs
0
0
0
0
0
0
0
0
0
0
0
Probability of Sell out
Probability
of Sell Out
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
Number of Standard Deviations
50%
Normal Distribution
0.45
Set order Qty to this many std. devs
0.4
Probability we
stock out =
Probability
demand exceeds
over qty =
0.86
0.35
Probability
we discount
last item =
0.3
0.25
Probability
demand is
smaller than
order
quantity =
0.2
0.15
Std Dev.s
0.1
0.05
0.14
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
What’s Wrong with This?
What else should we be looking at?
Still just worried about
Order up to 10,000
One order cycle
No minimum order qty.
A Second Idea
Look at 1 Product
How to trade off risks of overstock
(discounting) vs risks of understock (lost
sales)?
If we order Q
The last item faces what risk of being discounted?
Probability Demand < Q = F(Q)
The last item faces what risk of selling out
Probability Demand > Q = 1 - F(Q)
We want to be indifferent
We want two to be equal
Expected loss from Overstock = CO*F(Q)
Expected loss from Lost Sale = CL*(1-F(Q))
A little Algebra:
F(Q) = CL/(CO+CL)
Example
Oversimplification
Lost Sale: CL = Selling Price - Cost
Discount: CO = Cost - Salvage Value
Electra:
Selling Price $173
Cost
$ 50
Salvage
$ 0
Lost Sale: CL = $123
Discount: CO = 50
Want Probability of Discount = F(Q) = 123/173 = 0.71
Balancing Risks
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
Forecast
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Probability of
Style
Sell Out
Gail
0.86
Isis
0.86
Entice
0.86
Assault
0.86
Teri
0.86
Electra
0.86
Stephanie
0.86
Seduced
0.86
Anita
0.86
Daphne
0.86
Std Deviation in
Demand
388
646
496
680
762
807
1,048
1,113
2,094
1,394
Total Production
Expect Cost of
Lost Sale
$
51.33
$
41.92
$
25.67
$
34.22
$
62.45
$
105.23
$
71.01
$
19.68
$
36.79
$
83.84
Order
Amount
Std. Devs
606
(1.06)
357
(1.06)
832
(1.06)
1,804
(1.06)
292
(1.06)
1,294
(1.06)
2
(1.06)
2,837
(1.06)
1,075
(1.06)
905
(1.06)
10,003
-1.0605
Probability of Sell out
Probability
Last Item
is
Discounted
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
Expect Cost of
Discount
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
$
7.22
Salvage
Price
Cost
Value
$
110 $
50 $
$
99 $
50 $
$
80 $
50 $
$
90 $
50 $
$
123 $
50 $
$
173 $
50 $
$
133 $
50 $
$
73 $
50 $
$
93 $
50 $
$
148 $
50 $
Number of Standard Deviations
86%
Ratio
Rec. Ord. Q
0.55
1,061.30
0.49
1,033.82
0.38
1,199.95
0.44
2,430.00
0.59
1,280.25
0.71
2,598.90
0.62
1,444.34
0.32
3,481.05
0.46
3,098.17
0.66
2,966.21
20,593.99
Expect
Probability
Assoc. Std Probability Cost of Last Item is
Dev
of Sell Out Lost Sale Discounted
0.11
0.45 $ 27.27
0.55
(0.01)
0.51 $ 24.75
0.49
(0.32)
0.62 $ 18.75
0.38
(0.14)
0.56 $ 22.22
0.44
0.24
0.41 $ 29.67
0.59
0.56
0.29 $ 35.55
0.71
0.32
0.38 $ 31.20
0.62
(0.48)
0.68 $ 15.75
0.32
(0.09)
0.54 $ 23.12
0.46
0.42
0.34 $ 33.11
0.66
Expect
Cost of
Discount
$ 27.27
$ 24.75
$ 18.75
$ 22.22
$ 29.67
$ 35.55
$ 31.20
$ 15.75
$ 23.12
$ 33.11
Additional Thoughts
What’s the derivative of the cost as a
function of order quantity?
Expected Cost of Discounting Last Item
(increases with order size) - Expected
Cost of Stocking Out (decreases with
order size)
Decrease Order with largest estimated
derivative
Estimated Derivative
Style
Gail
Isis
Entice
Assault
Teri
Electra
Stephanie
Seduced
Anita
Daphne
Mean
Forecast
1,017
1,042
1,358
2,525
1,100
2,150
1,113
4,017
3,296
2,383
Std Deviation in
Demand
388
646
496
680
762
807
1,048
1,113
2,094
1,394
Total Production
Order
Amount
1,060
1,033
1,199
2,429
1,279
2,598
1,443
3,480
3,097
2,965
20,584
Probability of
Sell Out
0.46
0.51
0.63
0.56
0.41
0.29
0.38
0.69
0.54
0.34
Expect Cost
of Lost Sale
$
27.33
$
24.78
$
18.77
$
22.25
$
29.71
$
35.60
$
31.23
$
15.76
$
23.13
$
33.13
Probability
Last Item is
Discounted
0.54
0.49
0.37
0.44
0.59
0.71
0.62
0.31
0.46
0.66
Expect
Cost of
Discount
$
27.22
$
24.72
$
18.71
$
22.19
$
29.65
$
35.53
$
31.18
$
15.74
$
23.11
$
33.10
Estimated
Derivative
$
(0.11)
$
(0.06)
$
(0.06)
$
(0.05)
$
(0.06)
$
(0.07)
$
(0.05)
$
(0.02)
$
(0.02)
$
(0.04)
2-Rounds
What additional Issues?
What rules of thumb?
Only order late
Surely order early
Differences in Suppliers
Hong Kong
Higher Cost
Smaller Minimums
Faster
What rules of Thumb?
