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Parallel Machine Scheduling, Linear Programming, and Parameter List Scheduling Heuristics

Author

Listed:
  • Lap Mui Ann Chan

    (University of Toronto, Ontario, Canada)

  • Ana Muriel

    (University of Michigan, Ann Arbor, Michigan)

  • David Simchi-Levi

    (Northwestern University, Chicago, Illinois)

Abstract

In this paper we consider a class of parallel machine scheduling problems and their associated set-partitioning formulations. We show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics. This makes it possible to characterize the worst possible gap between optimal solutions for the scheduling problems and the corresponding linear programming relaxations. In the case of the classical parallel machine weighted completion time model we also show that the solution to the linear programming relaxation of the set-partitioning formulation is asymptotically optimal under mild assumptions on the distribution of job weights and processing times. Finally, we extend most of the results to the time-discretized formulation of machine scheduling problems.

Suggested Citation

  • Lap Mui Ann Chan & Ana Muriel & David Simchi-Levi, 1998. "Parallel Machine Scheduling, Linear Programming, and Parameter List Scheduling Heuristics," Operations Research, INFORMS, vol. 46(5), pages 729-741, October.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:5:p:729-741
    DOI: 10.1287/opre.46.5.729
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    References listed on IDEAS

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    1. Julien Bramel & David Simchi-Levi, 1997. "On the Effectiveness of Set Covering Formulations for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 45(2), pages 295-301, April.
    2. SOUSA, Jorge P. & WOLSEY, Laurence A., 1992. "A time indexed formulation of non-preemptive single machine scheduling problems," LIDAM Reprints CORE 984, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Jonathan F. Bard & Siwate Rojanasoonthon, 2006. "A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 24-44, February.
    2. J. G. Dai & Gideon Weiss, 2002. "A Fluid Heuristic for Minimizing Makespan in Job Shops," Operations Research, INFORMS, vol. 50(4), pages 692-707, August.
    3. Chung‐Yee Lee & Zhi‐Long Chen, 2000. "Scheduling jobs and maintenance activities on parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 145-165, March.
    4. Marjan van den Akker & Han Hoogeveen & Steef van de Velde, 2002. "Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 37-51, February.

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