Flexible ow 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 a renewable resource shared among the stages. The FFS scheduling problem is one of the most common manufacturing environments, 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, which can lead to a decrease in 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.