A computer manufacturer sells its laptop model through a web-based distributor, who buys at a unit cost of $200 and sells at a unit price of $500. The product life cycle is so short that the distributor is given only one opportunity to order stock before the technology becomes obsolete and a new model becomes available. At the beginning of the cycle, the distributor orders a stock level in the face of uncertain retail demand. Based on similar experiences in the past, the distributor believes that a reasonable demand model is a uniform distribution with a minimum of 1,000 and a maximum of 8,000 laptops. The items originally stocked are ultimately sold, returned, or scrapped. Customers place orders on the Web, and the distributor tries to satisfy their orders from stock. If there is a stock out, demands are lost.
The computer manufacturer offers the distributor a returns policy of the following form: It will pay $100 for each returned unit at the end of the product life cycle, but only up to a maximum of 20 percent of the original number of units ordered. Excess stock that cannot be returned to the manufacturer is picked up as scrap material by an electronics recycling center, with no cost or revenue involved. The decision facing the distributor is to choose an appropriate stock level.
a. Suppose there is no ceiling on the return of excess laptops. How many laptops should the distributor stock in order to maximize its expected profit?
b. With the returns ceiling in place, how many laptops should the distributor stock?
c. In part (b), what would be the maximum expected profit for the distributor?
d. What would be the corresponding expected profit for the manufacturer if the manufacturing cost is $125 per laptop, and the distributor uses the policy in part (b)?