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Two-agent scheduling on unrelated parallel machines with total completion time and weighted number of tardy jobs criteria

Author

Listed:
  • Yunqiang Yin

    (University of Electronic Science and Technology of China)

  • Youhua Chen

    (Department of Management Sciences, City University of Hong Kong)

  • Kaida Qin

    (Kunming University of Science and Technology)

  • Dujuan Wang

    (Business School, Sichuan University)

Abstract

This paper considers a two-agent scheduling problem in which each agent has a set of jobs that competes with that of another agent for the use of m unrelated parallel machines. Each agent aims to minimize a certain scheduling criterion related to the completion times of its jobs. The overall objective is to minimize the total completion time of the jobs of one agent while keeping the weighted number of tardy jobs of another agent within a given limit. We introduce a novel column generation scheme, called in-out column generation, to maintain the stability of dual variables and then embed this scheme into a branch-and-price framework. A greedy heuristic is used to obtain a set of initial columns to start the in-out column generation. The pricing subproblem in the column generation scheme is formulated as a single-machine scheduling problem that can be solved using dynamic programming techniques. An efficient branching strategy that is compatible with pricing subproblems is also proposed. The extensive computational results that are obtained by using randomly generated data demonstrate that our branch-and-price algorithm is singularly efficient and promising.

Suggested Citation

  • Yunqiang Yin & Youhua Chen & Kaida Qin & Dujuan Wang, 2019. "Two-agent scheduling on unrelated parallel machines with total completion time and weighted number of tardy jobs criteria," Journal of Scheduling, Springer, vol. 22(3), pages 315-333, June.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:3:d:10.1007_s10951-018-0583-z
    DOI: 10.1007/s10951-018-0583-z
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    References listed on IDEAS

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    Cited by:

    1. Tifenn Rault & Faiza Sadi & Jean-Charles Billaut & Ameur Soukhal, 2024. "Scheduling two interfering job sets on identical parallel machines with makespan and total completion time minimization," Journal of Scheduling, Springer, vol. 27(5), pages 485-505, October.
    2. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    3. Dujuan Wang & Yugang Yu & Huaxin Qiu & Yunqiang Yin & T. C. E. Cheng, 2020. "Two‐agent scheduling with linear resource‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 573-591, October.
    4. Oğuzhan Ahmet Arık, 2024. "Optimal policies for minimizing total job completion times and deviations from common due dates in unrelated parallel machine scheduling," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1654-1680, September.

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