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Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs

Author

Listed:
  • Yunqiang Yin

    (Kunming University of Science and Technology)

  • T. C. E. Cheng

    (The Hong Kong Polytechnic University)

  • Du-Juan Wang

    (Dalian Maritime University
    School of Management, University of Science and Technology of China
    China Business Executives Academy)

  • Chin-Chia Wu

    (Feng Chia University)

Abstract

We consider the scheduling problem in which two agents (agents A and B), each having its own job set (containing the A-jobs and B-jobs, respectively), compete to process their own jobs in a two-machine flowshop. Each agent wants to maximize a certain criterion depending on the completion times of its jobs only. Specifically, agent A desires to maximize either the weighted number of just-in-time (JIT) A-jobs that are completed exactly on their due dates or the maximum weight of the JIT A-jobs, while agent B wishes to maximize the weighted number of JIT B-jobs. Evidently four optimization problems can be formulated by treating the two agents’ criteria as objectives and constraints of the corresponding optimization problems. We focus on the problem of finding the Pareto-optimal schedules and present a bicriterion analysis of the problem. Solving this problem also solves the other three problems of bicriterion scheduling as a by-product. We show that the problems under consideration are either polynomially or pseudo-polynomially solvable. In addition, for each pseudo-polynomial-time solution algorithm, we show how to convert it into a two-dimensional fully polynomial-time approximation scheme for determining an approximate Pareto-optimal schedule. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms.

Suggested Citation

  • Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:4:d:10.1007_s10951-017-0511-7
    DOI: 10.1007/s10951-017-0511-7
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    References listed on IDEAS

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    Cited by:

    1. Vahid Nasrollahi & Ghasem Moslehi & Mohammad Reisi-Nafchi, 2022. "Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem," Operational Research, Springer, vol. 22(2), pages 1403-1442, April.
    2. Byung-Cheon Choi & Myoung-Ju Park, 2020. "Scheduling two projects with controllable processing times in a single-machine environment," Journal of Scheduling, Springer, vol. 23(5), pages 619-628, October.
    3. Matan Atsmony & Gur Mosheiov, 2023. "Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection," Journal of Scheduling, Springer, vol. 26(2), pages 193-207, April.
    4. Yuan Zhang & Zhichao Geng & Jinjiang Yuan, 2020. "Two-Agent Pareto-Scheduling of Minimizing Total Weighted Completion Time and Total Weighted Late Work," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    5. Enrique Gerstl & Gur Mosheiov, 2023. "A note: maximizing the weighted number of Just-in-Time jobs for a given job sequence," Journal of Scheduling, Springer, vol. 26(4), pages 403-409, August.
    6. Baruch Mor & Gur Mosheiov, 2022. "Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection," Operational Research, Springer, vol. 22(3), pages 2707-2719, July.

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