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Maximising the Total Weight of On-Time Jobs on Parallel Machines Subject to a Conflict Graph

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Mathematical Optimization Theory and Operations Research (MOTOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12755))

Abstract

The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the total weight of on-time jobs. The problem is known to be strongly NP-hard in general. A polynomial-time algorithm for scheduling unit execution time jobs on two machines is proposed. The performance of a broad family of approximation algorithms for scheduling unit execution time jobs on more than two machines is analysed. For the case of arbitrary job processing times, two integer linear programming formulations are proposed and compared with two formulations known from the earlier literature. An iterated variable neighborhood search algorithm is also proposed and evaluated by means of computational experiments.

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Author information

Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, Australia

    Yakov Zinder & Charlie Peter

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    Joanna Berlińska

Authors
  1. Yakov Zinder
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  2. Joanna Berlińska
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  3. Charlie Peter
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Corresponding author

Correspondence to Joanna Berlińska .

Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia

    Alexander Kazakov

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Zinder, Y., Berlińska, J., Peter, C. (2021). Maximising the Total Weight of On-Time Jobs on Parallel Machines Subject to a Conflict Graph. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_19

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  • DOI: https://doi.org/10.1007/978-3-030-77876-7_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77875-0

  • Online ISBN: 978-3-030-77876-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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