A fluid approach to large volume job shop scheduling
 Yoni Nazarathy,
 Gideon Weiss
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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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 Title
 A fluid approach to large volume job shop scheduling
 Journal

Journal of Scheduling
Volume 13, Issue 5 , pp 509529
 Cover Date
 20101001
 DOI
 10.1007/s1095101001740
 Print ISSN
 10946136
 Online ISSN
 10991425
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Job shops
 Makespan
 Stochastic scheduling
 Fluid approximation
 Fluid tracking policy
 Industry Sectors
 Authors

 Yoni Nazarathy ^{(1)}
 Gideon Weiss ^{(2)}
 Author Affiliations

 1. The Department of Mechanical Engineering and EURANDOM, Eindhoven University of Technology, Eindhoven, The Netherlands
 2. The Department of Statistics, The University of Haifa, Haifa, Israel