Multi-objective distributed reentrant permutation flow shop scheduling with sequence-dependent setup time

The distributed reentrant permutation flow shop (DRPFS) is a combination of the reentrant flow shop problem and distributed scheduling. The DRPFS is a NP-hard problem that consists of two subproblems: (1) assigning a set of jobs to a set of available factories and (2) determining the operation sequence of jobs in each factory. This paper is the first study to consider the inclusion of sequence-dependent setup time in the DRPFS. The industrial applications of flow shop indicate that the machine setup time to process a job may depend on the previously processed jobs. Particularly, in DRPFS, the effect of sequence-dependent setup time is intensified due to its reentrant characteristic. An improved version of the multi-objective adaptive large neighborhood search (MOALNS) is proposed as a solution method for the sequence-dependent DRPFS with the aim to minimize the makespan, production cost, and tardiness. The proposed algorithm enhances the standard MOALNS by embedding an improved solution acceptance and non-dominated set updating criteria to assist the algorithm in finding the near-optimal Pareto front of the factory allocation and scheduling problems. To address the multiple objectives and the issue of non-uniform setup time, a new set of destroy and repair heuristics are developed. Further, the numerical experiments demonstrate the efficiency of IMOALNS in finding high-quality solutions in a relatively short time.