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Model approximation for batch flow shop scheduling with fixed batch sizes

Author(s)
Weyerman, W. Samuel; Rai, Anurag; Warnick, Sean
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.
Date issued
2014-06
URI
http://hdl.handle.net/1721.1/104879
Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
Discrete Event Dynamic Systems
Publisher
Springer US
Citation
Weyerman, W. Samuel, Anurag Rai, and Sean Warnick. “Model Approximation for Batch Flow Shop Scheduling with Fixed Batch Sizes.” Discrete Event Dynamic Systems 25.4 (2015): 497–529.
Version: Author's final manuscript
ISSN
0924-6703
1573-7594

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