Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends

•We reviewed the Multi-objective Flow Shop Scheduling Problem literature in details.•The review showed that MOFSP arouses attention over time.•We found that the recent studies focus on contemporary heuristic algorithms.•Another common research direction is multi-objective modeling.

The flow shop scheduling problem is finding a sequence given n jobs with same order at m machines according to certain performance measure(s). The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, many real-world scheduling problems are multi-objective by nature. Over the years there have been several approaches used to deal with the multi-objective flow shop scheduling problems (MOFSP). Hence, in this study, we provide a brief literature review of the contributions to MOFSP and identify areas of opportunity for future research.