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Minimizing maximum tardiness and number of tardy jobs on parallel machines subject to minimum flow-time

Author

Listed:
  • J N D Gupta

    (University of Alabama in Huntsville)

  • A J Ruiz-torres

    (Polytechnic University of Puerto Rico)

  • S Webster

    (Syracuse University)

Abstract

This paper considers the problems of scheduling jobs on parallel identical machines where an optimal schedule is defined as one that gives the smallest maximum tardiness (or the minimum number of tardy jobs) among the set of schedules with optimal total flow-time (the sum of the completion times of all jobs). We show that these problems are unary NP-Hard, develop lower bounds for these two secondary criteria problems, and describe heuristic algorithms for their solution. Results of a computational study show that the proposed heuristic algorithms are quite effective and efficient in solving these hierarchical criteria scheduling problems.

Suggested Citation

  • J N D Gupta & A J Ruiz-torres & S Webster, 2003. "Minimizing maximum tardiness and number of tardy jobs on parallel machines subject to minimum flow-time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(12), pages 1263-1274, December.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:12:d:10.1057_palgrave.jors.2601638
    DOI: 10.1057/palgrave.jors.2601638
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    References listed on IDEAS

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    1. M Azizoglu & M Koksalan & S K Koksalan, 2003. "Scheduling to minimize maximum earliness and number of tardy jobs where machine idle time is allowed," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 661-664, June.
    2. S Rojanasoonthon & J F Bard & S D Reddy, 2003. "Algorithms for parallel machine scheduling: a case study of the tracking and data relay satellite system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 806-821, August.
    3. Chen, Chuen-Lung & Bulfin, Robert L., 1993. "Complexity of single machine, multi-criteria scheduling problems," European Journal of Operational Research, Elsevier, vol. 70(1), pages 115-125, October.
    4. J N D Gupta & J C Ho & S Webster, 2000. "Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(11), pages 1330-1339, November.
    5. Ho, Johnny C. & Chang, Yih-Long, 1995. "Minimizing the number of tardy jobs for m parallel machines," European Journal of Operational Research, Elsevier, vol. 84(2), pages 343-355, July.
    6. Nagar, Amit & Haddock, Jorge & Heragu, Sunderesh, 1995. "Multiple and bicriteria scheduling: A literature survey," European Journal of Operational Research, Elsevier, vol. 81(1), pages 88-104, February.
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    Citations

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    Cited by:

    1. Ruiz-Torres, Alex J. & Lopez, Francisco J. & Ho, Johnny C., 2007. "Scheduling uniform parallel machines subject to a secondary resource to minimize the number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 179(2), pages 302-315, June.
    2. C Gagné & M Gravel & W L Price, 2005. "Using metaheuristic compromise programming for the solution of multiple-objective scheduling problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 687-698, June.
    3. 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.
    4. Gupta, J.N.D. & Ruiz-Torres, Alex J., 2005. "Generating efficient schedules for identical parallel machines involving flow-time and tardy jobs," European Journal of Operational Research, Elsevier, vol. 167(3), pages 679-695, December.
    5. A J Ruiz-Torres & F J López & P J Wojciechowski & J C Ho, 2010. "Parallel machine scheduling problems considering regular measures of performance and machine cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 849-857, May.
    6. S-O Shim & Y-D Kim, 2007. "Minimizing total tardiness in an unrelated parallel-machine scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 346-354, March.
    7. Wenchang Luo & Rylan Chin & Alexander Cai & Guohui Lin & Bing Su & An Zhang, 2022. "A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 690-722, August.

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