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Minimizing Mean Squared Deviation of Completion Times About a Common Due Date

Author

Listed:
  • Uttarayan Bagchi

    (College of Business Administration, University of Texas, Texas 78712)

  • Robert S. Sullivan

    (College of Business Administration, University of Texas, Texas 78712)

  • Yih-Long Chang

    (Ohio State University, Columbus, Ohio 43210)

Abstract

This paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time. The scheduling objective is to minimize mean squared deviation (MSD) of job completion times about the due date. This nonregular measure of performance is appropriate when earliness and tardiness are both penalized, and when large deviations of completion time from the due date are undesirable. A special case of the MSD problem, referred to as the unconstrained MSD problem, is shown to be equivalent to the completion time variance problem (CTV) studied by Merten and Muller (Merten, A. G., M. E. Muller. 1972. Variance minimization in single machine sequencing problems. Management Sci. 18(September) 518--528.) and Schrage (Schrage, L. 1975. Minimizing the time-in-system variance for a finite jobset. Management Sci. 21(May) 540--543.). Strong results for this latter problem are combined with several new propositions to develop a reasonably efficient procedure for solving the unconstrained MSD problem. This enables us to improve the existing procedures for the CTV problem. We also propose a branching procedure for the constrained MSD problem and present computational results.

Suggested Citation

  • Uttarayan Bagchi & Robert S. Sullivan & Yih-Long Chang, 1987. "Minimizing Mean Squared Deviation of Completion Times About a Common Due Date," Management Science, INFORMS, vol. 33(7), pages 894-906, July.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:7:p:894-906
    DOI: 10.1287/mnsc.33.7.894
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    Citations

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    Cited by:

    1. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    2. Manna, D. K. & Prasad, V. Rajendra, 1999. "Bounds for the position of the smallest job in completion time variance minimization," European Journal of Operational Research, Elsevier, vol. 114(2), pages 411-419, April.
    3. Pereira, Jordi & Vásquez, Óscar C., 2017. "The single machine weighted mean squared deviation problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 515-529.
    4. X. Cai & F. S. Tu, 1996. "Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early‐tardy penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1127-1146, December.
    5. Rabia Nessah & Chengbin Chu, 2008. "A Lower Bound for the Weighted Completion Time Variance Problem," Working Papers 2008-ECO-16, IESEG School of Management, revised May 2010.
    6. Nessah, Rabia & Chu, Chengbin, 2010. "A lower bound for weighted completion time variance," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1221-1226, December.
    7. Gowrishankar, K. & Rajendran, Chandrasekharan & Srinivasan, G., 2001. "Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date," European Journal of Operational Research, Elsevier, vol. 132(3), pages 643-665, August.
    8. Awi Federgruen & Gur Mosheiov, 1993. "Simultaneous optimization of efficiency and performance balance measures in single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(7), pages 951-970, December.
    9. Srirangacharyulu, B. & Srinivasan, G., 2013. "An exact algorithm to minimize mean squared deviation of job completion times about a common due date," European Journal of Operational Research, Elsevier, vol. 231(3), pages 547-556.
    10. Ng, C. T. & Cai, X. & Cheng, T. C. E., 1996. "A tight lower bound for the completion time variance problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 211-213, July.
    11. Gajpal, Yuvraj & Rajendran, Chandrasekharan, 2006. "An ant-colony optimization algorithm for minimizing the completion-time variance of jobs in flowshops," International Journal of Production Economics, Elsevier, vol. 101(2), pages 259-272, June.
    12. Sridharan, V. & Zhou, Z., 1996. "A decision theory based scheduling procedure for single-machine weighted earliness and tardiness problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 292-301, October.
    13. Koulamas, Christos & Kyparisis, George J., 2023. "Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 608-616.
    14. Joseph Y.‐T. Leung, 2002. "A dual criteria sequencing problem with earliness and tardiness penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 422-431, June.
    15. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    16. Adamopoulos, G. I. & Pappis, C. P., 1996. "Scheduling jobs with different, job-dependent earliness and tardiness penalties using the SLK method," European Journal of Operational Research, Elsevier, vol. 88(2), pages 336-344, January.
    17. Adamopoulos, G. I. & Pappis, C. P., 1995. "The CON due-date determination method with processing time-dependent lateness penalties," International Journal of Production Economics, Elsevier, vol. 40(1), pages 29-36, June.
    18. Weng, Xiaohua & Ventura, Jose A., 1996. "Scheduling about a given common due date to minimize mean squared deviation of completion times," European Journal of Operational Research, Elsevier, vol. 88(2), pages 328-335, January.
    19. Mittenthal, John & Raghavachari, M. & Rana, Arif I., 1995. "V- and GG-shaped properties for optimal single machine schedules for a class of non-separable penalty functions," European Journal of Operational Research, Elsevier, vol. 86(2), pages 262-269, October.
    20. Seo, Jong Hwa & Kim, Chae-Bogk & Lee, Dong Hoon, 2001. "Minimizing mean squared deviation of completion times with maximum tardiness constraint," European Journal of Operational Research, Elsevier, vol. 129(1), pages 95-104, February.
    21. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.

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