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Scheduling unit time jobs with integer release dates to minimize the weighted number of tardy jobs

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  • Mitre Dourado
  • Rosiane Rodrigues
  • Jayme Szwarcfiter

Abstract

Consider a set of n unit time jobs, each one having a release date, a due date, both nonnegative integers, and a weight, a positive real number. Given a set of m parallel machines, we describe an algorithm for finding schedules with minimum weighted number of tardy jobs. The complexity of the proposed algorithm is $O(n^{2}\frac{(1+\log m)}{m})$ . The best previous algorithm for this problem has complexity O(mn 3 ) and employs network flow techniques. Our method is based on a characterization for schedules of this type and employs graph theoretic tools. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Mitre Dourado & Rosiane Rodrigues & Jayme Szwarcfiter, 2009. "Scheduling unit time jobs with integer release dates to minimize the weighted number of tardy jobs," Annals of Operations Research, Springer, vol. 169(1), pages 81-91, July.
    • Handle: RePEc:spr:annopr:v:169:y:2009:i:1:p:81-91:10.1007/s10479-008-0479-y
    DOI: 10.1007/s10479-008-0479-y
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    References listed on IDEAS

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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
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    Cited by:

    1. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    2. Peter Brucker & Natalia V. Shakhlevich, 2016. "Necessary and sufficient optimality conditions for scheduling unit time jobs on identical parallel machines," Journal of Scheduling, Springer, vol. 19(6), pages 659-685, December.
    3. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.

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