Selection of an optimal subset of sizes

For a company that produces a product in a range of sizes, it is sometimes possible to meet demand for a smaller size by substituting a larger size. In this paper, we give an integer linear programming model that addresses this issue. Various characteristics of the optimal policy are given. These properties are exploited when the formulation is extended to the multi-period stochastic demand case. This application was motivated by our experience with a company that manufactures a range of multiple-piece blind fasteners where savings in setup cost can be made using long-grip fasteners to meet the demand for short-grip fasteners.