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A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

Author

Listed:
  • Chi To Ng

    (The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Tai Chiu Edwin Cheng

    (The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Andrei M Bandalouski

    (National Academy of Sciences of Belarus, Minsk, Belarus)

  • Mikhail Y Kovalyov

    (National Academy of Sciences of Belarus, Minsk, Belarus)

  • Sze Sing Lam

    (The Open University of Hong Kong, Kowloon, Hong Kong)

Abstract

We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.

Suggested Citation

  • Chi To Ng & Tai Chiu Edwin Cheng & Andrei M Bandalouski & Mikhail Y Kovalyov & Sze Sing Lam, 2014. "A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(10), pages 1571-1579, October.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:10:p:1571-1579
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    Cited by:

    1. Martin Branda & Štěpán Hájek, 2017. "Flow-based formulations for operational fixed interval scheduling problems with random delays," Computational Management Science, Springer, vol. 14(1), pages 161-177, January.

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