A Simultaneous Worker Assignment and Scheduling Problem to Minimize Makespan in Flexible Flow Shop via Metaheuristic Approaches

In many real scheduling situations, it is necessary to deal with the worker assignment and job scheduling together. However, in traditional scheduling problems, only the machine is assumed to be a constraint and there isn’t any constraint about workers. This assumption could be due to the lower cost of workers compared to machines or the complexity of workers' assignment problems. This research proposes a flexible flow shop scheduling problem with two simultaneous issues: finding the best worker assignment, and solving the corresponding scheduling problem. We present a mathematical model that extends flexible flow shop scheduling problem to admit the worker assignment. Due to the NP-hardness of the research problem, two approximation approaches based on particle swarm optimization, named PSO and SPSO, are applied to minimize the makespan. The experimental results show that the proposed algorithms can efficiently minimize the makespan but the SPSO generates better solutions especially for large-size problems.