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A Parametric Worst Case Analysis of the LPT Heuristic for Two Uniform Machines

Author

Listed:
  • Paul Mireault

    (University of Montreal, Quebec, Canada)

  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Rakesh V. Vohra

    (Ohio State University, Columbus, Ohio)

Abstract

We consider the problem of minimizing the makespan when scheduling tasks on two uniform parallel machines, where one machine is q times as efficient on each task as is the other. We compute the maximum relative error of the LPT (largest processing time first) heuristic as an explicit function of q . In the special case that the two machines are identical ( q = 1), our problem and heuristic reduce to the problem and heuristic analyzed by Graham (Graham, R. 1969. Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17 416–429.).

Suggested Citation

  • Paul Mireault & James B. Orlin & Rakesh V. Vohra, 1997. "A Parametric Worst Case Analysis of the LPT Heuristic for Two Uniform Machines," Operations Research, INFORMS, vol. 45(1), pages 116-125, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:116-125
    DOI: 10.1287/opre.45.1.116
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    Citations

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    Cited by:

    1. 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.
    2. Koulamas, Christos & Kyparisis, George J., 2009. "A modified LPT algorithm for the two uniform parallel machine makespan minimization problem," European Journal of Operational Research, Elsevier, vol. 196(1), pages 61-68, July.
    3. Christos Koulamas & George J. Kyparisis, 2006. "A heuristic for maximizing the number of on‐time jobs on two uniform parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 568-575, September.
    4. Federico Della Croce & Rosario Scatamacchia, 2020. "The Longest Processing Time rule for identical parallel machines revisited," Journal of Scheduling, Springer, vol. 23(2), pages 163-176, April.
    5. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.
    6. Ivar Massabò & Giuseppe Paletta & Alex J. Ruiz-Torres, 2016. "A note on longest processing time algorithms for the two uniform parallel machine makespan minimization problem," Journal of Scheduling, Springer, vol. 19(2), pages 207-211, April.
    7. Qian Cao & Zhaohui Liu, 2010. "Semi-online scheduling with known maximum job size on two uniform machines," Journal of Combinatorial Optimization, Springer, vol. 20(4), pages 369-384, November.
    8. Alan J. Soper & Vitaly A. Strusevich, 2021. "Parametric analysis of the quality of single preemption schedules on three uniform parallel machines," Annals of Operations Research, Springer, vol. 298(1), pages 469-495, March.
    9. Liao, Ching-Jong & Lin, Chien-Hung, 2003. "Makespan minimization for two uniform parallel machines," International Journal of Production Economics, Elsevier, vol. 84(2), pages 205-213, May.

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