A Binary, Non-convex, Variable-capacitated Supply Chain Model

Abstract

This paper is concerned with three-echelon supply chain design where each supplier provides a unique set of goods from known, possibly multiple, locations and where each outlet has a fixed, known demand so that it exhibits the features of the supply chain of an existing company that operates across Canada and in the United States of America (35 suppliers, 83 potential DC locations and 2, 976 outlets). A mathematical model is presented whose so-lution determines the location and capacity level of Distribution Centers (DCs) and assigns outlets to the selected DCs. The model is unique in that it allows true variability in the choice of capacity level and so avoids the need to determine, a priori, a set of potential capacity levels. The design objective is to minimize fixed and variable costs for operations and transportation that ac-count for decreasing marginal costs and economies of scale. This makes the model a binary, non-convex optimization problem. A piecewise linear approxi-mation to the concave cost functions that captures the concept of “technology break-points” results in a model for which LINGO can quickly determine high quality solutions.