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A first Fit type algorithm for the coupled task scheduling problem with unit execution time and two exact delays

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  • Békési, József
  • Dósa, György
  • Galambos, Gábor

Abstract

The considered coupled task problem (CTP) is to schedule n jobs, each consisting of two (sub)tasks, on a single machine. Exact delay times are between the subtasks of a job and the makespan has to be minimized. It has been proven that the problem is strongly NP-hard in general case (see Orman and Potts (1997)), even if the lengths of the subtasks are identical. This paper considers a special case of CTP where there are jobs with two different delay times only. The complexity status of this problem is unknown. We will present an algorithm – called First Fit Decreasing (FFD) – and we will prove that its approximation ratio is in the interval (1.57894,1.57916).

Suggested Citation

  • Békési, József & Dósa, György & Galambos, Gábor, 2022. "A first Fit type algorithm for the coupled task scheduling problem with unit execution time and two exact delays," European Journal of Operational Research, Elsevier, vol. 297(3), pages 844-852.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:3:p:844-852
    DOI: 10.1016/j.ejor.2021.06.002
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    References listed on IDEAS

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    1. Dino Ahr & József Békési & Gábor Galambos & Marcus Oswald & Gerhard Reinelt, 2004. "An exact algorithm for scheduling identical coupled tasks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 193-203, June.
    2. Orman, A. J. & Potts, C. N. & Shahani, A. K. & Moore, A. R., 1996. "Scheduling for a multifunction phased array radar system," European Journal of Operational Research, Elsevier, vol. 90(1), pages 13-25, April.
    3. Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2020. "Coupled task scheduling with exact delays: Literature review and models," European Journal of Operational Research, Elsevier, vol. 282(1), pages 19-39.
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    Cited by:

    1. David Fischer & Péter Györgyi, 2023. "Approximation algorithms for coupled task scheduling minimizing the sum of completion times," Annals of Operations Research, Springer, vol. 328(2), pages 1387-1408, September.
    2. Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.

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