Metaheuristics for solving a flexible flow-shop scheduling problem with s-batching machines

Abstract

A scheduling problem for a two-stage flexible flow shop with s-batching machines motivated by processes in additive manufacturing is considered. A batch is a group of jobs that are processed together on a single machine. Each job belongs to an incompatible family. Only jobs of the same family can be batched together. A maximum batch size is given. A setup time occurs between different batches. The jobs of a batch are processed in a serial manner, that is, the processing time of a batch is the sum of the processing times of the jobs forming the batch. Batch availability is assumed. A job has a weight, a due date, and a release date. The total weighted tardiness is considered as performance measure. We establish a mixed integer linear programming formulation for this scheduling problem. For large-sized problem instances, an iterative decomposition approach (IDA) is proposed that uses a grouping genetic algorithm or an iterated local search (ILS) scheme to solve the single-stage subproblems. Moreover, an alternative ILS scheme based on a disjunctive graph representation of the problem at hand is designed. Results of computational experiments based on randomly generated problem instances demonstrate that the IDA hybridized with ILS outperforms the two other schemes.