Makespan Minimization in the Flow-shop Scheduling Problem with Sequence Dependent Setup Times
نویسندگان
چکیده
In this paper, we address the problem of finding a permutation schedule of n jobs in an m machine flow-shop environment that minimizes the maximum completion time Cmax (Makespan) of all jobs. The jobs are available at time zero and have sequence-dependent setup times on each machine. All parameters, such as processing and setup times, are assumed to be known with certainty. This problem is classified in the scheduling literature as the sequence-dependent setup time flow-shop (SDST flow shop) . It is easy to see that the SDST flow shop scheduling problem to minimize the Makespan is NP-hard in the strong sense, since the problem is equivalent to the extensively studied and computationally intractable travelling salesman problem (TSP) when m=1 [1]. Further, when sequence dependent setups are present on all machines of a flow shop, Gupta and Darrow [3] showed that permutation schedules (where the sequence of job on all stages is identical) are not always optimal even for the two-machine case.
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