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Uniform Parallel Machine Scheduling Problem with Controllable Delivery Times

Author

Listed:
  • Li Kai
  • Li Hui
  • Cheng Bayi

    (School of Management, Hefei University of Technology, Hefei230009, China)

  • Luo Qing

    (Nanling Branch, China Mobile Group Anhui Co., Ltd., Nanling242400, China)

Abstract

This paper considers the uniform parallel machine scheduling problem with controllable delivery times, which assumes that the delivery times of jobs are linear decreasing functions of the consumed resource. It aims to minimize the maximum completion time under the constraint that the total resource consumption does not exceed a given limit. For this NP-hard problem, we propose a resource allocation algorithm, named RAA, according to the feasible solution of the uniform parallel machine scheduling problem with fixed delivery times. It proves that RAA algorithm can obtain the optimal resource allocation scheme for any given scheduling scheme in O(n log n)time. Some algorithms based on heuristic algorithm LDT, heuristic algorithm LPDT and simulated annealing are proposed to solve the uniform parallel machine scheduling problem with controllable delivery times. The accuracy and efficiency of the proposed algorithms are tested based on those data with problem sizes varying from 40 to 200 jobs and 2 to 8 machines. The computational results indicate that the SA approach is promising and capable of solving large-scale problems in a reasonable time.

Suggested Citation

  • Li Kai & Li Hui & Cheng Bayi & Luo Qing, 2015. "Uniform Parallel Machine Scheduling Problem with Controllable Delivery Times," Journal of Systems Science and Information, De Gruyter, vol. 3(6), pages 525-537, December.
    • Handle: RePEc:bpj:jossai:v:3:y:2015:i:6:p:525-537:n:4
    DOI: 10.1515/JSSI-2015-0525
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    References listed on IDEAS

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    1. Kai Li & Shan-Lin Yang & Ming-Lun Ren, 2011. "Single‐machine scheduling problem with resource dependent release dates to minimise total resource‐consumption," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1811-1820.
    2. Janiak, Adam, 1991. "Single machine scheduling problem with a common deadline and resource dependent release dates," European Journal of Operational Research, Elsevier, vol. 53(3), pages 317-325, August.
    3. Nodari Vakhania, 2004. "Single-Machine Scheduling with Release Times and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 253-271, July.
    4. Lancia, Giuseppe, 2000. "Scheduling jobs with release dates and tails on two unrelated parallel machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 120(2), pages 277-288, January.
    5. M. Drozdowski & W. Kubiak, 1999. "Scheduling parallel tasks withsequential heads and tails," Annals of Operations Research, Springer, vol. 90(0), pages 221-246, January.
    6. Mohamed Haouari & Anis Gharbi, 2004. "Lower Bounds for Scheduling on Identical Parallel Machines with Heads and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 187-204, July.
    7. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
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    Cited by:

    1. Morgunov, V.I. (Моргунов, В.И.), 2016. "The Liquidity Management of the Banking Sector and the Short-Term Money Market Interest Rates [Управление Ликвидностью Банковского Сектора И Краткосрочной Процентной Ставкой Денежного Рынка]," Working Papers 21311, Russian Presidential Academy of National Economy and Public Administration.

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