Question

School Spirit (SS) is a retail store that sells Case Western Reserve University apparel. Suppose that it is April now and SS needs to decide how many commencement sweatshirts to order from the supplier. The entire demand for the commencement sweatshirt occurs during May. SS buys the sweatshirt from the supplier at $30 per shirt and sells it at $45. If SS runs out of the commencement sweatshirts, 35% of the customers who could not find the commencement sweatshirt will buy the regular Case sweatshirt instead. The remaining 65% of those customers will go to another store. The profit margin of the regular Case sweatshirt is $8. At the end of May, if any commencement sweatshirts are left in the inventory, SS will sell all of them at a discount price of $15.

Assume that the demand for the commencement sweatshirts in May is uniformly distributed between 400 and 500.

1. How many commencement sweatshirts should SS stock in April? (15 points)

Answer 1

Cost of underage, Cu = Selling price - Purchase cost = 45 - 30 = 15
Cost of overage, Co = Purchase cost - expected salvage value - expected revenue from the regular sweatshirts = 30 - 0.65*15 - 0.35*(30+8) = 6.95

Optimal in-stock probability = Cu / (Co + Cu) = 15 / (6.95+15) = 0.6834

So,

Optimal stocking level = 400 + 0.6834*(500-400) = 468 units