Stock selection heuristics for interdependent items

In a distribution environment, the problem of choosing the best mix of items to stock frequently involves considerations of interdependencies between the items. We address the problem of selecting a subset of items to stock from among a large set of potential items, when the objective is to maximize net revenue subject to a budget constraint, and when the items may be options, complements, or substitutes for one another. We develop a nonlinear integer programming model for this stock selection problem, and propose heuristic methods for its solution. Computational testing with randomly generated problem instances indicates the practical viability of this approach for rationalizing stock choice.