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

Abstract

This paper addresses 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 based on two concepts: (1) A failure probability of a job on a machine; and (2) A descent rate that reduces processing times for the 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 to generate 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 and, secondly, on 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.