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A Fully Polynomial Approximation Scheme for the Weighted Earliness–Tardiness Problem

Author

Listed:
  • Mikhail Y. Kovalyov

    (Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus)

  • Wieslaw Kubiak

    (École Nationale Supérieure de Génie Industriel, Laboratoire GILCO, and Université Joseph Fourier, Laboratoire Leibniz, Grenoble, France)

Abstract

A fully polynomial approximation scheme for the problem of scheduling n jobs on a single machine to minimize total weighted earliness and tardiness is presented. A new technique is used to develop the scheme. The main feature of this technique is that it recursively computes lower and upper bounds on the value of partial optimal solutions. Therefore, the scheme does not require any prior knowledge of lower and upper bounds on the value of a complete optimal solution. This distinguishes it from all the existing approximation schemes.

Suggested Citation

  • Mikhail Y. Kovalyov & Wieslaw Kubiak, 1999. "A Fully Polynomial Approximation Scheme for the Weighted Earliness–Tardiness Problem," Operations Research, INFORMS, vol. 47(5), pages 757-761, October.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:5:p:757-761
    DOI: 10.1287/opre.47.5.757
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    References listed on IDEAS

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    1. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
    2. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.
    3. M. Y. Kovalyov & C. N. Potts & L. N. van Wassenhove, 1994. "A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 86-93, February.
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    Citations

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    Cited by:

    1. Chuanli Zhao & Hengyong Tang, 2016. "Scheduling Deteriorating Jobs with Availability Constraints to Minimize the Makespan," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-10, December.
    2. 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.
    3. Kellerer, Hans & Rustogi, Kabir & Strusevich, Vitaly A., 2020. "A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date," Omega, Elsevier, vol. 90(C).
    4. Kubiak, Wieslaw & Cheng, Jinliang & Kovalyov, Mikhail Y., 2002. "Fast fully polynomial approximation schemes for minimizing completion time variance," European Journal of Operational Research, Elsevier, vol. 137(2), pages 303-309, March.
    5. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    6. Ming Liu & Feifeng Zheng & Chengbin Chu & Jiantong Zhang, 2012. "An FPTAS for uniform machine scheduling to minimize makespan with linear deterioration," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 483-492, May.
    7. Hendel, Yann & Sourd, Francis, 2006. "Efficient neighborhood search for the one-machine earliness-tardiness scheduling problem," European Journal of Operational Research, Elsevier, vol. 173(1), pages 108-119, August.
    8. Esteve, B. & Aubijoux, C. & Chartier, A. & T'kindt, V., 2006. "A recovering beam search algorithm for the single machine Just-in-Time scheduling problem," European Journal of Operational Research, Elsevier, vol. 172(3), pages 798-813, August.
    9. Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
    10. Ji, Min & Cheng, T.C.E., 2008. "Parallel-machine scheduling with simple linear deterioration to minimize total completion time," European Journal of Operational Research, Elsevier, vol. 188(2), pages 342-347, July.
    11. Min Ji & Chou-Jung Hsu & Dar-Li Yang, 2013. "Single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity consideration," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 437-447, October.
    12. Ji, Min & Cheng, T.C.E., 2010. "Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan," European Journal of Operational Research, Elsevier, vol. 202(1), pages 90-98, April.
    13. 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.
    14. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    15. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.

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