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A fluid approach to large volume job shop scheduling

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Abstract

We consider large volume job shop scheduling problems, in which there is a fixed number of machines, a bounded number of activities per job, and a large number of jobs. In large volume job shops it makes sense to solve a fluid problem and to schedule the jobs in such a way as to track the fluid solution. There have been several papers which used this idea to propose approximate solutions which are asymptotically optimal as the volume increases. We survey some of these results here. In most of these papers it is assumed that the problem consists of many identical copies of a fixed set of jobs. Our contribution in this paper is to extend the results to the far more general situation in which the many jobs are all different. We propose a very simple heuristic which can schedule such problems. We discuss asymptotic optimality of this heuristic, under a wide range of previously unexplored situations. We provide a software package to explore the performance of our policy, and present extensive computational evidence for its effectiveness.

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Authors and Affiliations

  1. The Department of Mechanical Engineering and EURANDOM, Eindhoven University of Technology, Eindhoven, The Netherlands

    Yoni Nazarathy

  2. The Department of Statistics, The University of Haifa, Haifa, Israel

    Gideon Weiss

Authors
  1. Yoni Nazarathy
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  2. Gideon Weiss
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Correspondence to Gideon Weiss.

Additional information

Research supported in part by Israel Science Foundation Grant 249/02 and 454/05 and by European Network of Excellence Euro-NGI.

Part of this research was conducted while Yoni Nazarathy was a student at the University of Haifa.

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Nazarathy, Y., Weiss, G. A fluid approach to large volume job shop scheduling. J Sched 13, 509–529 (2010). https://doi.org/10.1007/s10951-010-0174-0

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