Abstract
This article addresses the job-shop scheduling problem of minimizing the length of a schedule (makespan) for processing n jobs by one or two machines with sequence-dependent setup times and clean-up times. The processing of each job includes at most two operations that have to be non-preemptive. Machine routes may differ from job to job. If all setup and clean-up times are equal to zero, this problem is polynomially solvable via Jackson's pair of job permutations, otherwise it is NP-hard even if each of n jobs consists of one operation on the same machine. We present sufficient conditions when Jackson's pair of job permutations may be used for solving the two-machine job-shop scheduling problem with sequence-dependent setup times and clean-up times. For the general case of the latter problem, the results obtained provide polynomial lower and upper bounds for the objective function which may be used in an implicit enumeration technique, e.g., in a branch-and-bound algorithm.
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