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The Single Machine Problem with a Quadratic Cost Function of Completion Times

Author

Listed:
  • Wlodzimierz Szwarc

    (School of Business Administration, University of Wisconsin, Milwaukee, Wisconsin 53201)

  • Marc E. Posner

    (Industrial and Systems Engineering Department, Ohio State University, Columbus, Ohio 43210)

  • John J. Liu

    (School of Business Administration, University of Wisconsin, Milwaukee, Wisconsin 53201)

Abstract

This paper examines a single machine sequencing problem with a quadratic cost function of completion times. A new type of precedence relation is constructed that determines the ordering between adjacent jobs. Each pair of jobs has a critical start time, after which the precedence relation changes direction. These relations are incorporated into a solution procedure that solved 191 out of 200 test problems with job sizes ranging from 15 to 100 without using enumeration methods. Although 9 problems were not solved directly by the procedure, even these were reduced to 10 much smaller problems (of the job sizes 3 and 4) which could easily be solved by inspection.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:12:p:1480-1488
    DOI: 10.1287/mnsc.34.12.1480
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    Citations

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    Cited by:

    1. Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    2. Cheng, T. C. Edwin & Shakhlevich, Natalia V., 2005. "Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 165(2), pages 444-456, September.
    3. 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.
    4. J-B Wang & J-J Wang & P Ji, 2011. "Scheduling jobs with chain precedence constraints and deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1765-1770, September.
    5. Szwarc, Wlodzimierz & Mukhopadhyay, Samar K., 1996. "Solution of the generalized Townsend single machine scheduling model," European Journal of Operational Research, Elsevier, vol. 91(1), pages 203-210, May.
    6. Schaller, Jeffrey, 2002. "Minimizing the sum of squares lateness on a single machine," European Journal of Operational Research, Elsevier, vol. 143(1), pages 64-79, November.

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