Approximation algorithms for the three-stage flexible flow shop problem with mid group constraint

• We propose ten heuristics for that problem and give their time complexities.
• We give 4 lower bounds for that problem and worst case rates of nine heuristics.
• We design a computational experiment to test the performance of ten heuristics.
• SP.JH-MJ is best and TSM is the worst among the ten heuristics by the experiment.

This paper considers a three-stage flexible flow shop scheduling problem, where the jobs have the group constraint at the second stage and the three stages consist of unrelated parallel machines. Because of the complexity of this problem, approximation algorithms are more appropriate to solve it. Firstly, we propose ten heuristic algorithms based on the idea of combined algorithms proposed by Soewandi and Elmaghraby (2001) and give their time complexities. Secondly, since there is no reference on the worst-case performance ratios of RDM, SP.H1 and SP.H2 algorithms for the unrelated parallel machines, we provide the worst-case performance ratios of these three algorithms and then give the worst-case performance ratios of the nine algorithms proposed in this paper. Finally, to evaluate the performance of the ten algorithms, four lower bounds of this problem are proposed in Appendix A and a computational experiment is designed, where lots of instances are generated and each algorithm is run with every instance. Experimental results indicate that the performances of ten heuristic algorithms are contingent on different configurations and SP.JH-MJ algorithm generally outperforms the others with respect to the three-stage flexible flow shop scheduling problem addressed in this paper.