Abstract In a recent paper a quadratic mixed-integer programming model was presented for an industrial purchasing problem involving complicated discount structures. The solution method presented in the paper for this model involved the solution of a series of quadratic zero-one programming problems. The disadvantages of such an approach are immediately obvious to anyone familiar with the state-of-the-art of solution methods for nonlinear integer programming problems. In this paper a linear model is constructed for the same problem and its computational advantages over the nonlinear model are discussed.