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Adjacent orderings in single‐machine scheduling with earliness and tardiness penalties

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  • Wlodzimierz Szwarc

Abstract

This article deals with a single‐machine n job earliness‐tardiness model with job‐independent penalties. It demonstrates that the arrangement of adjacent jobs in an optimal schedule depends on a critical value of the start times. Based on these precedence relations, the article develops criteria under which the problem can be decomposed into smaller subproblems. The branching scheme that used the developed results was tested on 70 examples of size n = 10. This scheme should be incorporated in any branch‐and‐bound method once a lower bound is found. The branching scheme can easily handle small problems without a lower bound. © 1993 John Wiley & Sons, Inc.

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  • Wlodzimierz Szwarc, 1993. "Adjacent orderings in single‐machine scheduling with earliness and tardiness penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 229-243, March.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:2:p:229-243
    DOI: 10.1002/1520-6750(199303)40:23.0.CO;2-R
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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. Wlodzimierz Szwarc & Marc E. Posner & John J. Liu, 1988. "The Single Machine Problem with a Quadratic Cost Function of Completion Times," Management Science, INFORMS, vol. 34(12), pages 1480-1488, December.
    3. Wlodzimierz Szwarc, 1989. "Single‐machine scheduling to minimize absolute deviation of completion times from a common due date," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 663-673, October.
    4. Uttarayan Bagchi & Yih‐Long Chang & Robert S. Sullivan, 1987. "Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 739-751, October.
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    1. Jaw‐Yeh Chen & Sheng‐Fuu Lin, 2002. "Minimizing weighted earliness and tardiness penalties in single‐machine scheduling with idle time permitted," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 760-780, December.
    2. Vincent T’kindt & Karima Bouibede-Hocine & Carl Esswein, 2007. "Counting and enumeration complexity with application to multicriteria scheduling," Annals of Operations Research, Springer, vol. 153(1), pages 215-234, September.
    3. Schaller, Jeffrey & Valente, Jorge M.S., 2020. "Minimizing total earliness and tardiness in a nowait flow shop," International Journal of Production Economics, Elsevier, vol. 224(C).

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