Hybrid matheuristics to solve the integrated lot sizing and scheduling problem on parallel machines with sequence-dependent and non-triangular setup

TL;DR

This paper introduces hybrid matheuristics combining relax-and-fix, fix-and-optimize, path-relinking, and kernel search heuristics to effectively solve the complex ILSSP-NT on parallel machines, outperforming traditional solvers.

Contribution

The study develops novel hybrid matheuristics specifically designed for the ILSSP-NT with sequence-dependent setup costs and times on parallel machines, filling a gap in the literature.

Findings

Matheuristics outperform CPLEX in most instances

Proposed methods effectively handle complex setup costs and capacities

Significant reduction in solution time and costs achieved

Abstract

This paper approaches the integrated lot sizing and scheduling problem (ILSSP), in which non-identical machines work in parallel with non-triangular sequence-dependent setup costs and times, setup carry-over and capacity limitation. The aim of the studied ILSSP, here called ILSSP-NT on parallel machines, is to determine a production planning and tasks sequencing that meet period demands without delay and in such a way that the total costs of production, machine setup and inventory are minimized. The dearth of literature on the ILSSP-NT, despite the increasing amount of applications in the industrial sector, mainly in the food processing industry, motivated us to conduct this study. In this paper, we propose efficient methods to solve the ILSSP-NT on parallel machines. The methods virtually consist in the hybridization of the relax-and-fix and fix-and-optimize methods with the path-relinking and kernel search heuristics. To assess how well the heuristics solve the ILSSP-NT on parallel machines, we compared their results with those of the CPLEX solver with a fixed CPU time limit. The proposed matheuristics significantly outperformed CPLEX in most of the tested instances.