Optimal retail assortments for substitutable items purchased in sets

We consider the problem of optimizing assortments in a multi-item retail inventory system. In addition to the usual holding and stockout costs, there is a fixed cost for including any item in the assortment. Customers' preferences for items include both probabilistic substitution patterns and the desire to purchase sets of complementary items. We develop a demand model to capture this behavior, and derive tractable approximations that allow us to formulate the optimization problem as a 0-1 mixed integer linear program. Numerical examples are solved to illustrate key insights into how both complementary and substitute items affect the optimal assortment and the expected profit. (C) 2003 Wiley Periodicals, Inc.