A bi-objective multi-item capacitated lot-sizing model: Two Pareto-based meta-heuristic algorithms

Abstract

Lot-sizing problems (LSP) form a class of production planning problems in which available quantities are always considered as decision variables in the production plan. The goal of this paper is to present a multi-item capacitated lot-sizing problem (MICLSP) with setup times, safety stock deficit costs, demand shortage costs – both backorder and lost sale states – and different manners of production. Although a considerable amount of research has concentrated on model development and solution procedures in the terms of single-objective problems in the past decade, to make the model more realistic this paper develops a bi-objective mathematical programming model with two conflicting objectives including: (1) minimizing the total cost considered by the production plans including production costs with different manners of production, inventory costs, safety stock deficit costs, shortage costs and setup costs; (2) minimizing the required storage space. Considering that the proposed model is NP-hard, we propose two novel Pareto-based multi-objective meta-heuristic algorithms called multi-objective vibration damping optimization (MOVDO) and the non-dominated ranking genetic algorithm (NRGA) for the literature on LSP. In order to validate the performance of the proposed MOVDO and NRGA, a non-dominated sorting genetic algorithm (NSGA-II), one of the most common multi-objective meta-heuristic algorithms, is applied. The optimal solutions are also reported to justify the results. Finally, we calibrate both algorithms by robust response surface methodology (RSM); then, the results are analysed on some test problems, both graphically and statistically.