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One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons

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  • John J. Kanet

    (Department of Management Information Systems, Operations Management, and Decision Sciences, University of Dayton, Dayton, Ohio 45469)

Abstract

In 1969 H. Emmons provided three theorems (Emmons 1--3) for determining precedence relations between pairs of jobs for the single-machine tardiness problem. We show here a fourth straightforward theorem that uses the information when the jobs in the pair are both known to precede a third job in an optimum sequence. The new theorem augments the three Emmons theorems and is shown to be a generalization of a theorem by Elmaghraby.

Suggested Citation

  • John J. Kanet, 2014. "One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 62(2), pages 345-347, April.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:2:p:345-347
    DOI: 10.1287/opre.2013.1253
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    References listed on IDEAS

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    1. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    2. Kenneth R. Baker & Linus E. Schrage, 1978. "Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks," Operations Research, INFORMS, vol. 26(1), pages 111-120, February.
    3. Chris N. Potts & Luk N. Van Wassenhove, 1985. "A Branch and Bound Algorithm for the Total Weighted Tardiness Problem," Operations Research, INFORMS, vol. 33(2), pages 363-377, April.
    4. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    5. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    6. A. H. G. Rinnooy Kan & B. J. Lageweg & J. K. Lenstra, 1975. "Minimizing Total Costs in One-Machine Scheduling," Operations Research, INFORMS, vol. 23(5), pages 908-927, October.
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    Cited by:

    1. John J. Kanet & Federico Della Croce & Christos Koulamas & Vincent T’kindt, 2015. "Erratum—One Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 63(2), pages 351-352, April.

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