The Effect of Individual Representation on the Performance of a Genetic Algorithm applied to a Supply Chain Network Design Problem

Abstract

This paper presents a comparison of a variety of individual representations in a procedure based on the Genetic Algorithm for a capacitated model for supply chain network design (SCND) that considers the cost of quality (COQ) as well as the traditional manufacturing and distribution costs. The model is known as the SCND-COQ and can be used at a strategic planning level to maximize profit subject to meeting an overall quality level. The SCND-COQ model internally computes quality costs for the whole supply chain considering the interdependencies among business entities, whereas previous works have assumed exogenously and independently given COQ functions (nonlinear functions). The SCND-COQ model is a constrained mixed-integer nonlinear programming problem (MINLP) which is challenging to solve because it combines all the difficulties of both of its subcategories: the combinatorial nature of mixed integer programming and the difficulty of solving non-convex nonlinear problems. The aim is to maximize the profit of the supply chain subject to: demand, capacity, flow balance, and overall quality level of the final product constraints. We provide a solution method based on the genetic algorithm (GA) for solving instances of practical and realistic size. We compare the performance of the GA with several individual representations and a greedy constructive heuristic procedure. Managerial insights for practitioners are provided and the results of computational testing are reported.