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A characterization of optimal multiprocessor schedules and new dominance rules

Author

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  • Rico Walter

    (Friedrich Schiller University Jena)

  • Alexander Lawrinenko

    (Friedrich Schiller University Jena)

Abstract

The paper on hand approaches the classical makespan minimization problem on identical parallel machines from a rather theoretical point of view. Using an approach similar to the idea behind inverse optimization, we identify a general structural pattern of optimal multiprocessor schedules. We also show how to derive new dominance rules from the characteristics of optimal solutions. Results of our computational study attest to the efficacy of the new rules. They are particularly useful in limiting the search space when each machine processes only a few jobs on average.

Suggested Citation

  • Rico Walter & Alexander Lawrinenko, 2020. "A characterization of optimal multiprocessor schedules and new dominance rules," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 876-900, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00634-9
    DOI: 10.1007/s10878-020-00634-9
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    References listed on IDEAS

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    1. Walter, Rico & Wirth, Martin & Lawrinenko, Alexander, 2017. "Improved approaches to the exact solution of the machine covering problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 80530, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Mokotoff, Ethel, 2004. "An exact algorithm for the identical parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 152(3), pages 758-769, February.
    3. Christos Koulamas, 2005. "Inverse scheduling with controllable job parameters," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 1(1), pages 35-43.
    4. Mauro Dell'Amico & Manuel Iori & Silvano Martello & Michele Monaci, 2008. "Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 333-344, August.
    5. Federico Della Croce & Rosario Scatamacchia & Vincent T’kindt, 2019. "A tight linear time $$\frac{13}{12}$$ 13 12 -approximation algorithm for the $$P2 || C_{\max }$$ P 2 | | C max problem," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 608-617, August.
    6. Mauro Dell’Amico & Silvano Martello, 1995. "Optimal Scheduling of Tasks on Identical Parallel Processors," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 191-200, May.
    7. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    8. Antonio Frangioni & Emiliano Necciari & Maria Grazia Scutellà, 2004. "A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 195-220, June.
    9. Jouglet, Antoine & Carlier, Jacques, 2011. "Dominance rules in combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 212(3), pages 433-444, August.
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