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Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product

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  • Kellerer, Hans
  • Strusevich, Vitaly

Abstract

We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizing the total weighted flow time with controllable processing times, minimizing the makespan with controllable release dates, minimizing the total weighted flow time for two models of scheduling with rejection.

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  • 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.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:1:p:24-32
    DOI: 10.1016/j.ejor.2012.12.028
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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. 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).
    2. Halman, Nir & Kellerer, Hans & Strusevich, Vitaly A., 2018. "Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 435-447.
    3. Dolgui, Alexandre & Kovalev, Sergey & Pesch, Erwin, 2015. "Approximate solution of a profit maximization constrained virtual business planning problem," Omega, Elsevier, vol. 57(PB), pages 212-216.
    4. Liqi Zhang & Lingfa Lu & Jinjiang Yuan, 2016. "Two-machine open-shop scheduling with rejection to minimize the makespan," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 519-529, March.
    5. Baruch Mor & Dana Shapira, 2022. "Single machine scheduling with non-availability interval and optional job rejection," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 480-497, August.
    6. Guojun Hu & Pengxiang Pan & Suding Liu & Ping Yang & Runtao Xie, 2024. "The prize-collecting single machine scheduling with bounds and penalties," Journal of Combinatorial Optimization, Springer, vol. 48(2), pages 1-13, September.
    7. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
    8. Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    9. Luo, Wenchang & Gu, Boyuan & Lin, Guohui, 2018. "Communication scheduling in data gathering networks of heterogeneous sensors with data compression: Algorithms and empirical experiments," European Journal of Operational Research, Elsevier, vol. 271(2), pages 462-473.
    10. Sergey Kovalev, 2015. "Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization," Annals of Operations Research, Springer, vol. 235(1), pages 815-819, December.
    11. 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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