The use of genetic algorithms to solve the economic lot size scheduling problem

Abstract

The purpose of this paper is to investigate the use genetic algorithms (GAs) for solving the Economic Lot Size Scheduling Problem (ELSP). The ELSP is formulated using the Basic Period (BP) approach which results in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced. This formulation is ideally suited for using GAs. The GA is tested on Bomberger's classical problem. The resulting solutions were better than those obtained using an iterative dynamic programming (DP) approach. The total cost of GA solutions to the problem with utilization up to 65% were within 3.4% of the lower bound. The GA also performed well for higher utilization yielding solutions within 13.87% of the lower bound for utilization up to 86%. The GA was tested on a 30-item problem and good solutions were obtained. The results of the GA under different binary representations, crossover methods, and initialization methods are compared to identify the best settings. The results indicate that for this particular problem, binary representation works better than Gray coding, 2-point crossover is best, and an infeasible starting population is better than feasible.