Ephemeral Apparel (EA) has been suffering from stockouts of some items and overstocks of other items. Robert Michaels, vice president of marketing, and Michael Roberts, EA’s new vice president of logistics, are battling over how to set inventory targets for several key product lines for the 2013 summer season. Orders must be placed in December 2012 to ensure that products will be available in EA distribution centers by May 2013. Michaels claims that the cost of customer goodwill for stocking out of any item should be set at two times the selling price of that item.

Further, he claims that because of this high cost of stocking out, the service target for all items should be a 95% probability of not stocking out in the season. Roberts says that these are overestimates and will cause EA to carry too much inventory. Accordingly, Roberts asked the Finance and Merchandising departments to provide some data to help him develop service level targets more scientifically. One particular item, for example, has a projected gross margin (per-unit profit margin divided by per-unitselling price) of 45% and a projected end-of-season salvage value of 20% of the per-unit cost. (Hint: You should be able to express all relevant costs in terms of the item’s price, p.)

a. If Logistics VP Roberts accepts Marketing VP Michaels’ estimate of goodwill cost, what is the best service level for this item?

b. If goodwill cost were estimated at five times the selling price of the item, what is the best service level for this item?

c. Given these results, what do you believe Mr. Roberts should recommend to Mr. Michaels regarding his proposed 95% service target?