An iterated greedy algorithm for distributed blocking flow shop with setup times and maintenance operations to minimize makespan

Abstract

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given by distributed flow shop scheduling problems and the addition of constraints to the problem. This article introduces the distributed blocking flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is developed to mathematically describe the problem and heuristic procedures are proposed to incorporate maintenance operations to job scheduling. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with sizes of 4,800 and 13,200 problems, respectively. Computational experiments were carried out to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.