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

We describe the purchasing decisions faced by a multi-plant company. The suppliers of this company offer complex discount schedules based on the total quantity (rather than cost) of ingredients purchased. The schedules simultaneously account both for corporate purchases and for purchases at the individual plant level. The complexity of the purchasing decisions is further increased due to the existence of alternative production recipes for each final product. We formulate the corresponding cost-minimization problem as a nonlinear mixed 0–1 programming problem. We propose various ways to linearize this formulation, and we evaluate the quality of the resulting models on real-world data.