Question

We are setting inventory policy in a Newsvendor situation. For the item in question, the full retail value is $105 and the wholesale cost is $64. For items not sold at full retail, we receive a salvage value of $12.

What is the critical fractile we should use in deciding on a stocking quantity? (Round your answer to 2 decimal places.)

Answer 1

The critical fractal for the Newsvendor model, given the costs, is 0.44. This means the stocking quantity should be set where the probability of selling all items is 44%.

Step-by-step explanation:

To calculate the critical fractal for the Newsvendor model, you need to consider both the costs of overstocking and understocking. The overstocking cost is the difference between the wholesale cost and the salvage value, whereas the understocking cost is the difference between the retail value and the wholesale cost. In this case, the overstocking cost is $64 - $12 = $52, and the understocking cost is $105 - $64 = $41.

To find the critical fractile, you use the formula:

Critical Fractal = Understocking Cost / (Understocking Cost + Overstocking Cost)

Plugging in the numbers:

Critical Fractal = $41 / ($41 + $52)
= $41 / $93

This results in a critical fractal of approximately 0.44.

Therefore, in deciding on a stocking quantity, you should stock such that the probability of selling all stock is 44%.