Optimal procurement decisions in the presence of total quantity discounts and alternative product recipes

We describe the cost-minimization problem faced by the purchasing department of a multi-plant company when its suppliers offer discounts based simultaneously on plant and on corporate purchases, when discount schedules depend on the total quantity (rather than cost) of ingredients purchased, and when alternative production recipes exist for each final product. We formulate the problem as a nonlinear mixed 0-1 programming problem and we propose various ways to linearize this formulation. The quality of these models is evaluated on real-world data.