Determining order quantities in multi-product inventory systems subject to multiple constraints and incremental discounts

This paper presents a mixed-integer programming model for ordering items in multi-product multi-constraint inventory systems from suppliers who offer incremental quantity discounts. The model is based on a piecewise linear approximation of the number of orders function. It allows any number of linear constraints and determines if independent or common (fixed) cycle ordering has a lower total cost. The paper discusses implementation issues and presents results of computational tests on example problems from the operational research literature as well as randomly generated test problems.