Abstract
This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M1,M2 and M_{3}. A job is first processed on M1 and then is assigned either the route (M2,M_{3}) or the route (M_{3},M2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(nlog n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value.
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Strusevich, V., Drobouchevitch, I. & Shakhlevich, N. Three-machine shop scheduling with partially ordered processing routes. J Oper Res Soc 53, 574–582 (2002). https://doi.org/10.1057/palgrave.jors.2601329
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DOI: https://doi.org/10.1057/palgrave.jors.2601329