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.