The Discrete Two-Dimensional Assortment Problem

In the two-dimensional assortment problem, a unit of product that is larger or better on two measurements or qualities may be used to substitute, at some cost, for a unit of demand that is smaller or inferior on both measurements or qualities. The problem is to determine which dimensional combinations to stock in order to minimize the combined stocking and substitution costs. Characteristics of the optimal stocking pattern are presented, and three heuristic solution procedures are compared with an optimization technique under a variety of conditions for demand and cost characteristics.