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Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

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  • Uttarayan Bagchi
  • Yih‐Long Chang
  • Robert S. Sullivan

Abstract

We consider a single‐machine scheduling problem in which all jobs have the same due date and penalties are assessed for both early and late completion of jobs. However, earliness and tardiness are penalized at different rates. The scheduling objective is to minimize either the weighted sum of absolute deviations (WSAD) or the weighted sum of squared deviations (WSSD). For each objective we consider two versions of the problem. In the unconstrained version an increase in the due date does not yield any further decrease in the objective function. We present a constructive algorithm for the unconstrained WSAD problem and show that this problem is equivalent to the two‐parallel, nonidentical machine, mean flow‐time problem. For the unconstrained WSSD and the constrained WSAD and WSSD problems we propose implicit enumeration procedures based on several dominance conditions. We also report on our computational experience with the enumeration procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:5:p:739-751
    DOI: 10.1002/1520-6750(198710)34:53.0.CO;2-3
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    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. 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.
    3. 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.
    4. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    5. 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.
    6. Alidaee, Bahram & Dragan, Irinel, 1997. "A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date," European Journal of Operational Research, Elsevier, vol. 96(3), pages 559-563, February.
    7. Sabuncuoglu, Ihsan & Lejmi, Tahar, 1999. "Scheduling for non regular performance measure under the due window approach," Omega, Elsevier, vol. 27(5), pages 555-568, October.
    8. Cai, X., 1995. "Minimization of agreeably weighted variance in single machine systems," European Journal of Operational Research, Elsevier, vol. 85(3), pages 576-592, September.
    9. Adamopoulos, George I. & Pappis, Costas P., 1996. "A fuzzy-linguistic approach to a multi-criteria sequencing problem," European Journal of Operational Research, Elsevier, vol. 92(3), pages 628-636, August.
    10. Xia, Yu & Chen, Bintong & Yue, Jinfeng, 2008. "Job sequencing and due date assignment in a single machine shop with uncertain processing times," European Journal of Operational Research, Elsevier, vol. 184(1), pages 63-75, January.
    11. Yue, Jinfeng & Wang, Min-Chiang & Chen, Bintong, 2007. "Mean-range based distribution-free procedures to minimize "overage" and "underage" costs," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1103-1116, January.
    12. John J. Clifford & Marc E. Posner, 2000. "High Multiplicity in Earliness-Tardiness Scheduling," Operations Research, INFORMS, vol. 48(5), pages 788-800, October.
    13. Cai, X. & Lum, V. Y. S. & Chan, J. M. T., 1997. "Scheduling about a common due date with kob-dependent asymmetric earliness and tardiness penalties," European Journal of Operational Research, Elsevier, vol. 98(1), pages 154-168, April.
    14. 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.
    15. Enrique Gerstl & Gur Mosheiov, 2014. "Single machine just‐in‐time scheduling problems with two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 1-16, February.
    16. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.
    17. Adamopoulos, George I. & Pappis, Costas P., 1998. "Scheduling under a common due-data on parallel unrelated machines," European Journal of Operational Research, Elsevier, vol. 105(3), pages 494-501, March.
    18. Gerhard J. Woeginger, 1999. "An Approximation Scheme for Minimizing Agreeably Weighted Variance on a Single Machine," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 211-216, May.
    19. Ventura, Jose A. & Radhakrishnan, Sanjay, 2003. "Single machine scheduling with symmetric earliness and tardiness penalties," European Journal of Operational Research, Elsevier, vol. 144(3), pages 598-612, February.
    20. 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.
    21. Zhi-Long Chen, 1997. "Scheduling with batch setup times and earliness-tardiness penalties," European Journal of Operational Research, Elsevier, vol. 96(3), pages 518-537, February.
    22. Yeong‐Dae Kim & Candace Arai Yano, 1994. "Minimizing mean tardiness and earliness in single‐machine scheduling problems with unequal due dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(7), pages 913-933, December.
    23. X. Cai & S. Zhou, 1997. "Scheduling stochastic jobs with asymmetric earliness and tardiness penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 531-557, September.
    24. Li, Lei & Fonseca, Daniel J. & Chen, Der-San, 2006. "Earliness-tardiness production planning for just-in-time manufacturing: A unifying approach by goal programming," European Journal of Operational Research, Elsevier, vol. 175(1), pages 508-515, November.

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