Models for Ordering Multiple Products Subject to Multiple Constraints, Quantity and Freight Discounts: Scientific Perspectives

One of the most important responsibilities of a supply chain manager is to decide “how much” (or
“many”) of inventory items to order and how to transport them. This paper presents four mixed-integer
linear programming models to help supply chain managers make these decisions for multiple
products subject to multiple constraints when suppliers offer quantity discounts and shippers offer
freight discounts. Each model deals with one of the possible combinations of all-units and incremental
quantity discounts and all-weight and incremental freight discounts. The models are based on a
piecewise linear approximation of the number of orders function. They allow any number of linear
constraints and determine if independent or common (fixed) cycle ordering has a lower total cost.
Results of computational experiments on an example problem are also presented.