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A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date

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  • Kellerer, Hans
  • Rustogi, Kabir
  • Strusevich, Vitaly A.

Abstract

We address the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date. This is a basic problem with applications to the just-in-time manufacturing. The problem is linked to a Boolean programming problem with a quadratic objective function, known as the half-product. An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the problem is identified and implemented. The running time matches the best known running time for an FPTAS for minimizing a half-product with no additive constant.

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  • 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).
    • Handle: RePEc:eee:jomega:v:90:y:2020:i:c:s0305048318306443
    DOI: 10.1016/j.omega.2018.11.001
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    References listed on IDEAS

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    1. Kellerer, Hans & Strusevich, Vitaly, 2013. "Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product," European Journal of Operational Research, Elsevier, vol. 228(1), pages 24-32.
    2. Janiak, Adam & Kovalyov, Mikhail Y. & Kubiak, Wieslaw & Werner, Frank, 2005. "Positive half-products and scheduling with controllable processing times," European Journal of Operational Research, Elsevier, vol. 165(2), pages 416-422, September.
    3. 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.
    4. 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.
    5. Yin, Yunqiang & Cheng, Shuenn-Ren & Cheng, T.C.E. & Wang, Du-Juan & Wu, Chin-Chia, 2016. "Just-in-time scheduling with two competing agents on unrelated parallel machines," Omega, Elsevier, vol. 63(C), pages 41-47.
    6. Xu, Zhou, 2012. "A strongly polynomial FPTAS for the symmetric quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 377-381.
    7. 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.
    8. T. Badics & E. Boros, 1998. "Minimization of Half-Products," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 649-660, August.
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    Cited by:

    1. Alidaee, Bahram & Li, Haitao & Wang, Haibo & Womer, Keith, 2021. "Integer programming formulations in sequencing with total earliness and tardiness penalties, arbitrary due dates, and no idle time: A concise review and extension," Omega, Elsevier, vol. 103(C).
    2. Sang, Yao-Wen & Wang, Jun-Qiang & Sterna, Małgorzata & Błażewicz, Jacek, 2023. "Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work," Omega, Elsevier, vol. 121(C).
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    5. Kasper, T.A. Arno & Land, Martin J. & Teunter, Ruud H., 2023. "Towards System State Dispatching in High‐Variety Manufacturing," Omega, Elsevier, vol. 114(C).
    6. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).

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