Multidimensional assortment problem with an application

This paper addresses the discrete multidimensional assortment problem. Assortment issues arise frequently in practice as an important design and inventory problem which simultaneously seeks the answers to two related questions: (a) Which items (or sizes of a product) to stock? (b) How much of each to stock? Its discrete multidimensional version concerns itself with choosing sizes from among a discrete set of possible ones with each size being characterized by more than one dimension. Our research is motivated by an application of the problem in the distribution center of a global manufacturer of telecommunications equipment where the goal was to standardize the sizes of three-dimensional crates used to package finished items by selecting a few from among all crate sizes. The main contributions of this research are (1) modeling the assortment problem as a facility location problem, (2) devising a heuristic procedure that generates a good solution to the problem as well as a bound on the optimal solution, and (3) implementing the heuristic procedure on a PC so as to obtain solutions for actual large-scale instances of a three-dimensional problem.