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Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time

Author

Listed:
  • Yong He

    (Zhejiang University)

  • Zhiyi Tan

    (Zhejiang University)

Abstract

This paper considers the on-line problem of scheduling nonpreemptively n independent jobs on m > 1 identical and parallel machines with the objective to maximize the minimum machine completion time. It is assumed that the values of the processing times are unknown but the order of the jobs by their processing times is known in advance. We are asked to decide the assignment of all the jobs to some machines at time zero by utilizing only ordinal data rather than the actual magnitudes of jobs. Algorithms to slove the problem are called ordinal algorithms. In this paper, we give lower bounds and ordinal algorithms. We first propose an algorithm MIN which is at most $$(\left\lceil {\sum {_{i = 1}^m {\text{ }}1/} i} \right\rceil + 1)$$ -competitive for any m machine case, while the lower bound is ∑ i=1 m 1/i. Both are on the order of Θ(ln m). Furthermore, for m = 3, we present an optimal algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:2:d:10.1023_a:1013855712183
    DOI: 10.1023/A:1013855712183
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    References listed on IDEAS

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    1. D. K. Friesen & B. L. Deuermeyer, 1981. "Analysis of Greedy Solutions for a Replacement Part Sequencing Problem," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 74-87, February.
    2. 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. Rico Walter, 2013. "Comparing the minimum completion times of two longest-first scheduling-heuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 125-139, January.
    2. 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.
    3. 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.
    4. Yiwei Jiang & Zhiyi Tan & Yong He, 2005. "Preemptive Machine Covering on Parallel Machines," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 345-363, December.

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