Question

In a Newsvendor Model setting, with random demand that follows a Normal distribution, the following information is available to you. During the last season, the cost of underage was equal to the cost of overage. The optimal ordering decision (to maximize the expected profit) was 25 units. However, this season, the cost of underage increased by 30%. (No other change.) As the result, the optimal ordering decision became 27 units. Using the aforementioned information, what is the mean and standard deviation of the demand? Note: Please refer the z-table wherever you deem necessary.

Answer 1

Cost of underage = Cu

Cost of overage = Co

Cu = Co

Service Level = = 0.5

For Service level of 0.5, Z value = 0

Let the Mean be X and std. Deviation be

Optimal Order Quantity = 25

Optimal Order Quantity = X + Z*

25 = X + 0*

X = 25 units

Case -2:

Cost of underage increased 30%

Cu = 1.3 * Co

Service Level = = = (1.3 / 2.3) = 0.5652

For Service Level = 0.5652, Z value = 0.15

Optimal Order Quantity = 27

Optimal Order Quantity = X + Z*

27 = 25 + 0.16*

= 12.5 units

Hence, Mean = 25 units, Std. Deviation = 12.5 units

(Note: In the second case, Z value may vary a little as it is rounded off)

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