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Parallel solutions for ordinal scheduling with a small number of machines

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  • Leah Epstein

    (University of Haifa)

Abstract

We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in advance. For problems with two parallel solutions, it is required to design two solutions, and the performance of an algorithm is tested for each input using the best solution of the two. We find tight results for makespan minimization on two and three machines, and algorithms that have strictly better competitive ratios than the best possible algorithm with a single solution also for four and five machines. To prove upper bounds, we use a new approach of considering pairs of machines from the two solutions.

Suggested Citation

  • Leah Epstein, 2023. "Parallel solutions for ordinal scheduling with a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-24, August.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:1:d:10.1007_s10878-023-01069-8
    DOI: 10.1007/s10878-023-01069-8
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    References listed on IDEAS

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    1. Yong He & Zhiyi Tan, 2002. "Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 199-206, June.
    2. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    3. N. V. R. Mahadev & Aleksandar Pekeč & Fred S. Roberts, 1998. "On the Meaningfulness of Optimal Solutions to Scheduling Problems: Can an Optimal Solution be Nonoptimal?," Operations Research, INFORMS, vol. 46(3-supplem), pages 120-134, June.
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    Cited by:

    1. Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.

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