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On the Minimization of the Makespan Subject to Flowtime Optimality

Author

Listed:
  • Brian Thomas Eck

    (Juran Institute, Inc., Wilton, Connecticut)

  • Michael Pinedo

    (Columbia University, New York, New York)

Abstract

When scheduling n jobs on m identical machines in parallel, two performance criteria are of particular interest: the makespan (the completion time of the last job) and the flowtime (the sum of the completion times of all n jobs). Whereas minimizing makespan is NP-hard, many schedules minimize flowtime, and they are easy to characterize. This paper considers the problem of minimizing the makespan among flowtime-optimal schedules. Heuristics have appeared in the literature that result in flowtime-optimal schedules with makespans which are always less than or equal to 5/4 times the minimum flowtime-optimal makespan. In this note, we present new heuristics for this problem, one of which yields a worst-case bound of 28/27 for the two-machine case. The new heuristics have a running time of O ( n log n ). Extensions are discussed for general m .

Suggested Citation

  • Brian Thomas Eck & Michael Pinedo, 1993. "On the Minimization of the Makespan Subject to Flowtime Optimality," Operations Research, INFORMS, vol. 41(4), pages 797-801, August.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:4:p:797-801
    DOI: 10.1287/opre.41.4.797
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    Citations

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    Cited by:

    1. R-H Huang & C-L Yang & H-T Huang, 2010. "Parallel machine scheduling with common due windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 640-646, April.
    2. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    3. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2023. "Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time," European Journal of Operational Research, Elsevier, vol. 305(2), pages 594-607.
    4. Hesaraki, Alireza F. & Dellaert, Nico P. & de Kok, Ton, 2019. "Generating outpatient chemotherapy appointment templates with balanced flowtime and makespan," European Journal of Operational Research, Elsevier, vol. 275(1), pages 304-318.
    5. Lin, Yang-Kuei & Fowler, John W. & Pfund, Michele E., 2013. "Multiple-objective heuristics for scheduling unrelated parallel machines," European Journal of Operational Research, Elsevier, vol. 227(2), pages 239-253.
    6. Qian, Fubin & Strusevich, Vitaly & Gribkovskaia, Irina & Halskau, Øyvind, 2015. "Minimization of passenger takeoff and landing risk in offshore helicopter transportation: Models, approaches and analysis," Omega, Elsevier, vol. 51(C), pages 93-106.
    7. Peruvemba Sundaram Ravi & Levent Tunçel & Michael Huang, 2016. "Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime," Journal of Scheduling, Springer, vol. 19(5), pages 547-561, October.
    8. Myungho Lee & Kangbok Lee & Michael Pinedo, 2022. "Tight approximation bounds for the LPT rule applied to identical parallel machines with small jobs," Journal of Scheduling, Springer, vol. 25(6), pages 721-740, December.
    9. Gupta, Jatinder N. D. & Ruiz-Torres, Alex J., 2000. "Minimizing makespan subject to minimum total flow-time on identical parallel machines," European Journal of Operational Research, Elsevier, vol. 125(2), pages 370-380, September.

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