On the n-job, m-machine permutation flow shop scheduling problems with makespan criterion and rework

This paper addresses an n-job, m-machine permutation flow shop scheduling problem (PFSSP) with unlimited intermediate buffers and rework activities. The concept of rework means that processing of a job on a machine may not meet a predefined quality level through its first process. Thus we have a probabilistic cycle of operations for jobs on different machines which is based on two concepts: (1) a failure probability of a job on a machine and, (2) a descent rate that reduces the processing times for rework phase. In this case, the processing times of jobs on machines become random variables with a known probability distribution. The aim of this paper is to examine possible solution approaches for generating the efficient job sequences with the least potential makespan. A wide range of simulation-based approaches are applied to address the proposed problem. These methods contain mathematical formulation, heuristic algorithms, and metaheuristics. The mechanism of the solution approaches is based on firstly using expected processing times to find a job sequence; then evaluating the obtained job sequences by several simulated trials. Using the one-way ANOVA test, these methods have been compared together, and the results show the superiority of metaheuristics, especially simulated annealing, over the other methods