The flexible job shop scheduling problem: A review

•A review providing insights on the flexible job shop scheduling problem is proposed.•The makespan criterion is covered, but also alternative criteria and multi-criteria optimization.•Various constraints extending the problem are discussed.•Additional problem characteristics and solution approaches are surveyed.•Extensive research perspectives on the problem are motivated. The flexible job shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which has wide applications in the real world. The complexity and relevance of the FJSP have led to numerous research works on its modeling and resolution. This paper reviews some of the research of the past 30 years on the problem, by presenting and classifying the different criteria, constraints, configurations and solution approaches that have been considered. Recent emerging topics on complex shop scheduling, multi-criteria optimization and uncertain and dynamic environments are discussed. Finally, future research opportunities are proposed.