A Practical Model for Ordering in Multi-Product Multi-Constraint Inventory Systems with All-Units Quantity Discounts

Abstract

This paper presents a practical mathematical model for determining order quantities in multi-product multi-constraint inventory systems with all-units quantity discounts. The model is a zero-one mixed integer programming model based on a linear approximation of the number of orders function. The paper discusses issues of model implementation and presents computational testing results from solving randomly generated test problems with up to 100 products. It also presents computational data that compares the model’s performance to those of other approaches found in the operational research literature. The computational evidence suggests that the model finds identical and often better solutions than other approaches to the problems considered in the paper. These results indicate that the model is a viable alternative to other approaches found in the literature for the solution of the problem; but more importantly, they indicate that the model is a practical tool for decision makers who do not possess the resources necessary to implement and use specialized algorithms.