Flow shop scheduling with jobs arriving at different times

Flow shop scheduling is common in modern lean production systems. In practice, jobs in flow shops can arrive at irregular times. However, scheduling that considers such irregularity has not been adequately investigated in the literature. In this paper, we examine the scheduling of n-jobs in an m-machine permutation flow shop with an unlimited intermediate storage. The jobs in this shop are assumed to have deterministic and known occurrence times. The objective of this scheduling is to reduce the total completion time (F_m|prmu|∑C_j). To improve the quality of solution, we successively put each job in the current best position and reinsert certain jobs based on weight calculations. We then develop and compare the solutions obtained by our simple and constructive heuristic method against the optimal schedules or other simple heuristic solutions with and without jobs arriving at different times. The computational experiments highlight the efficiency, easy implementation, and excellent performance of our proposed heuristic method.