Two-Stage flowshop Scheduling Problems with Identical and Batch Processors

This paper considers minimizing total completion time in a two-stage flowshop scheduling problem with m identical parallel machines at Stage 1 and a batch processor at Stage 2. We prove that the problem when all jobs have same processing time at Stage 2 is NP – hard and gave a two-approximation algorithm in O(n3) time. In the case that all jobs have arbitrary processing time at Stage 1 and at Stage 2, we give an approximation algorithm after pointing out that in this case the problem is strongly NP – hard. Hundreds of instances of a numerical experiment show that the worst-case ratio of this approximation algorithm is nearing 2.

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