MAXIMIZING THE PROBABILITY OF ACHIEVING A TARGET PROFIT IN A TWO‐PRODUCT NEWSBOY PROBLEM*

Abstract

ABSTRACT This paper explores the two‐product newsboy problem. Solution procedures are developed to find the optimal production quantities of each product that will maximize the probability of achieving a profit target. The problem is shown to be surprisingly challenging, and numerical results obtained for only the more restrictive cases exhibit interesting behavior with important decision implications. For example, the results suggest that, if a firm has two single‐product divisions and each will receive a bonus for achieving a profit target, it is beneficial for the two divisions to cooperate if the targets are lax and the profit margins are high, but not if the targets are tight and the profit margins low. Also, between two products having different profit margins, one should produce more of the product with the lower profit margin if the target is sufficiently lax. This exploration motivates further efforts in solving the two‐product problem for the more general cases and also in extending the problem to three or more products.