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Lower Bounds for Uniform Machine Scheduling Using Decision Diagrams

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

We propose a relaxed decision diagram (DD) formulation for obtaining lower bounds on uniform machine scheduling instances, based on separators to separate jobs on different machines. Experiments on the total tardiness for instances with tight due times show that for obtaining nontrivial bounds, it is important to partition the DD nodes on a layer based on their machine finishing time. When the number of jobs is small, DDs provide stronger bounds in less time than a time-indexed LP relaxation.

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Notes

  1. 1.

    We use a slightly simpler definition, where \(L \subseteq \mathcal {J}\).

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Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands

    Pim van den Bogaerdt & Mathijs de Weerdt

Authors
  1. Pim van den Bogaerdt
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  2. Mathijs de Weerdt
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Correspondence to Pim van den Bogaerdt .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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van den Bogaerdt, P., de Weerdt, M. (2019). Lower Bounds for Uniform Machine Scheduling Using Decision Diagrams. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_38

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  • DOI: https://doi.org/10.1007/978-3-030-19212-9_38

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  • Online ISBN: 978-3-030-19212-9

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