A matheuristic based on column generation for parallel machine scheduling with sequence dependent setup times

Abstract

In this paper we propose a heuristic approach based on column generation (CG) and a general purpose integer programming (GPIP) solver to address a scheduling problem. The problem consists in scheduling independent jobs with given processing times on unrelated parallel machines with sequence-dependent setup times. The objective is to minimize the total weighted tardiness. The proposed matheuristic (MH) takes advantage of the efficiency of CG to define a (restricted) search space which is explored by a GPIP solver. In different iterations, different additional constraints are introduced in CG, allowing the definition of several (restricted) search spaces to be explored by the GPIP solver. Computational results show that the proposed MH can be used to tackle very large instances (e.g. 100 machines and 400 jobs) obtaining better solutions in less time than a state-of-the-art branch-and-price algorithm from the literature.