In this research, the flexible flow line scheduling problem with minimisation of makespan as the objective by considering constraints for the beginning and terminating times of processing the jobs at stages is investigated for the first time. The process of jobs at some stages cannot
be started before a specific time and should be completed before another specific time. Since the process of jobs at each stage should be performed at an interval time, in spite of regular scheduling problems, every schedule cannot be considered as a feasible solution. A mathematical model
is developed to solve the proposed research problem optimally. Since the research problem is shown to be NP-hard, several hybrid metaheuristic algorithms based on particle swarm optimisation (PSO) and simulated annealing (SA) are proposed to heuristically solve large-size problems. In these
algorithms, for each renewed particle in PSO algorithm, a local search is performed based on SA. The major difference among the proposed algorithms is the rules used to perform the local search. The performances of the proposed algorithms are compared based on randomly generated test problems.
Based on the results of this comparison, the best proposed metaheuristic algorithm has a good performance with the average percentage gap of 0.289% compared to the optimal solution for the test problems that can be solved optimally.
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