Sport Obermeyer

What to order?What are the issues?

A Sample Problem

Commit 10,000 units before showCommit 10,000 units after showMinimum of 600 units

A First Approach

Ignore differences in Profit margins Salvage values

Ignore minimum lot sizesConsider only first order cycle

Sample Problem

Style Mean Forecast Std Deviation in DemandGail 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

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-5 -4 -3 -2 -1 0 1 2 3 4 5

Std Dev.s

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 Mean

Forecast Std Deviation in

Demand Order

Amount Std. DevsProbability of Sell Out

Gail 1,017 388 1,017 0 0.50 Isis 1,042 646 1,042 0 0.50 Entice 1,358 496 1,358 0 0.50 Assault 2,525 680 2,525 0 0.50 Teri 1,100 762 1,100 0 0.50 Electra 2,150 807 2,150 0 0.50 Stephanie 1,113 1,048 1,113 0 0.50 Seduced 4,017 1,113 4,017 0 0.50 Anita 3,296 2,094 3,296 0 0.50 Daphne 2,383 1,394 2,383 0 0.50

Total Production 20,001 0 Number of Standard DeviationsProbability of Sell out 50%

Normal Distribution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-5 -4 -3 -2 -1 0 1 2 3 4 5

Std Dev.s

Probability we discount last item =

Probability demand is smaller than order quantity =

0.14

Set order Qty to this many std. devs

Probability we stock out =Probability demand exceeds over qty =0.86

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 QThe last item faces what risk of being

discounted?Probability Demand < Q = F(Q)

The last item faces what risk of selling outProbability Demand > Q = 1 - F(Q)

We want to be indifferent

We want two to be equalExpected loss from Overstock =

CO*F(Q)

Expected loss from Lost Sale = CL*(1-F(Q))

A little Algebra:F(Q) = CL/(CO+CL)

ExampleOversimplificationLost Sale: CL = Selling Price - Cost

Discount: CO = Cost - Salvage ValueElectra:

Selling Price $173 Cost $ 50 Salvage $ 0

Lost Sale: CL = $123

Discount: CO = 50Want Probability of Discount = F(Q) = 123/173 = 0.71Find Q with this cumulative probability: ~2,599

Balancing Risks Style

Mean Forecast

Std Deviation in Demand

Order Amount Std. Devs Price Cost

Salvage Value

Gail 1,017 388 606 (1.06) 110$ 50$ -$ Isis 1,042 646 357 (1.06) 99$ 50$ -$ Entice 1,358 496 832 (1.06) 80$ 50$ -$ Assault 2,525 680 1,804 (1.06) 90$ 50$ -$ Teri 1,100 762 292 (1.06) 123$ 50$ -$ Electra 2,150 807 1,294 (1.06) 173$ 50$ -$ Stephanie 1,113 1,048 2 (1.06) 133$ 50$ -$ Seduced 4,017 1,113 2,837 (1.06) 73$ 50$ -$ Anita 3,296 2,094 1,075 (1.06) 93$ 50$ -$ Daphne 2,383 1,394 905 (1.06) 148$ 50$ -$

Total Production 10,003 -1.0605 Number of Standard DeviationsProbability of Sell out 86%

Style Probability of

Sell OutExpect Cost of

Lost Sale

Probability Last Item

is Discounted

Expect Cost of Discount Ratio Rec. Ord. Q

Assoc. Std Dev

Probability of Sell Out

Expect Cost of

Lost Sale

Probability Last Item is Discounted

Expect Cost of

DiscountGail 0.86 51.33$ 0.14 7.22$ 0.55 1,061.30 0.11 0.45 27.27$ 0.55 27.27$ Isis 0.86 41.92$ 0.14 7.22$ 0.49 1,033.82 (0.01) 0.51 24.75$ 0.49 24.75$ Entice 0.86 25.67$ 0.14 7.22$ 0.38 1,199.95 (0.32) 0.62 18.75$ 0.38 18.75$ Assault 0.86 34.22$ 0.14 7.22$ 0.44 2,430.00 (0.14) 0.56 22.22$ 0.44 22.22$ Teri 0.86 62.45$ 0.14 7.22$ 0.59 1,280.25 0.24 0.41 29.67$ 0.59 29.67$ Electra 0.86 105.23$ 0.14 7.22$ 0.71 2,598.90 0.56 0.29 35.55$ 0.71 35.55$ Stephanie 0.86 71.01$ 0.14 7.22$ 0.62 1,444.34 0.32 0.38 31.20$ 0.62 31.20$ Seduced 0.86 19.68$ 0.14 7.22$ 0.32 3,481.05 (0.48) 0.68 15.75$ 0.32 15.75$ Anita 0.86 36.79$ 0.14 7.22$ 0.46 3,098.17 (0.09) 0.54 23.12$ 0.46 23.12$ Daphne 0.86 83.84$ 0.14 7.22$ 0.66 2,966.21 0.42 0.34 33.11$ 0.66 33.11$

20,593.99

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 Mean

Forecast Std Deviation in

Demand Order

AmountProbability of

Sell OutExpect Cost of Lost Sale

Probability Last Item is Discounted

Expect Cost of

DiscountEstimated Derivative

Gail 1,017 388 1,060 0.46 27.33$ 0.54 27.22$ (0.11)$ Isis 1,042 646 1,033 0.51 24.78$ 0.49 24.72$ (0.06)$ Entice 1,358 496 1,199 0.63 18.77$ 0.37 18.71$ (0.06)$ Assault 2,525 680 2,429 0.56 22.25$ 0.44 22.19$ (0.05)$ Teri 1,100 762 1,279 0.41 29.71$ 0.59 29.65$ (0.06)$ Electra 2,150 807 2,598 0.29 35.60$ 0.71 35.53$ (0.07)$ Stephanie 1,113 1,048 1,443 0.38 31.23$ 0.62 31.18$ (0.05)$ Seduced 4,017 1,113 3,480 0.69 15.76$ 0.31 15.74$ (0.02)$ Anita 3,296 2,094 3,097 0.54 23.13$ 0.46 23.11$ (0.02)$ Daphne 2,383 1,394 2,965 0.34 33.13$ 0.66 33.10$ (0.04)$

Total Production 20,584

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?