flexible flow shop scheduling problem to minimize makespan with renewable resources

This paper deals with a flexible flow shop (ffs) scheduling problem with unrelated parallel machines and renewable resource shared among the stages. the ffs scheduling problem is one of the most common manufacturing environment in which there is more than a machine in at least one production stage. in such a system, to decrease the processing times, additional renewable resources are assigned to the jobs or machines, and it can lead to decrease the total completion time. for this purpose, a mixed integer linear programming (milp) model is proposed to minimize the maximum completion time (makespan) in an ffs environment. the proposed model is computationally intractable. therefore, a particle swarm optimization (pso) algorithm as well as a hybrid pso and simulated annealing (sa) algorithm named sa-pso, are developed to solve the model. through numerical experiments on randomly generated test problems, the authors demonstrate that the hybrid sa-pso algorithm outperforms the pso, especially for large size test problems.