An Effective Multi-Objective Particle Swarm Optimization for the Multi-Item Capacitated Lot-Sizing Problem with Set-Up Times and Backlogging

ABSTRACT In this article, a multi-item capacitated lot-sizing problem (MICLSP) with consideration of set-up times and backlogging, which is one of the key issues in production planning, is addressed. The inventory is formulated as a separate objective function representing its level instead of integrating it into a total cost function for effective control of this objective. The proposed model attempts to minimize simultaneously the total cost and the total inventory level. The developed model shows high performance compared to its mono-objective version. An efficient multi-objective particle swarm optimization (MOPSO) is developed to generate a representative set of Pareto-optimal solutions. A numerical example is given to illustrate the application of the proposed algorithm. The algorithm’s effectiveness is proven based on two experiments conducted on a set of 28 instances. The experiments compare the proposed algorithm’s results with those of the augmented epsilon-constraint method and the basic version of MOPSO.