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Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications

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  • Hans Kellerer

    (Universität Graz)

  • Vitaly A. Strusevich

    (University of Greenwich)

Abstract

This paper reviews the problems of Boolean non-linear programming related to the half-product problem. All problems under consideration have a similar quadratic non-separable objective function. For these problems, we focus on the development of fully polynomial-time approximation schemes, especially of those with strongly polynomial time, and on their applications to various scheduling problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2018-y
    DOI: 10.1007/s10479-015-2018-y
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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. 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.
    4. Kabir Rustogi & Vitaly A. Strusevich, 2017. "Single machine scheduling with a generalized job-dependent cumulative effect," Journal of Scheduling, Springer, vol. 20(6), pages 583-592, December.
    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.

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