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A dual criteria sequencing problem with earliness and tardiness penalties

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  • Joseph Y.‐T. Leung

Abstract

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than ${3\over 2}$. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:4:p:422-431
    DOI: 10.1002/nav.10020
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    References listed on IDEAS

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    1. P. S. Sundararaghavan & Mesbah U. Ahmed, 1984. "Minimizing the sum of absolute lateness in single‐machine and multimachine scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 325-333, June.
    2. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1989. "Note---A Note on the Minimization of Mean Squared Deviation of Completion Times About a Common Due Date," Management Science, INFORMS, vol. 35(9), pages 1143-1147, September.
    3. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
    4. Sankaran Lakshminarayan & Ram Lakshmanan & Robert L. Papineau & Rene Rochette, 1978. "Technical Note—Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties," Operations Research, INFORMS, vol. 26(6), pages 1079-1082, December.
    5. Gupta, Sushil K. & Sen, Tapan, 1983. "Minimizing a quadratic function of job lateness on a single machine," Engineering Costs and Production Economics, Elsevier, vol. 7(3), pages 187-194, September.
    6. 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.
    7. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    8. Jeffrey B. Sidney, 1977. "Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties," Operations Research, INFORMS, vol. 25(1), pages 62-69, February.
    9. Hamilton Emmons, 1987. "Scheduling to a common due date on parallel uniform processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 803-810, December.
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