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Maximum latency scheduling problem on two-person cooperative games

Author

Listed:
  • Yanhong Gu

    (Shenzhen University)

  • Jing Fan

    (Shanghai Second Polytechnic University)

  • Guochun Tang

    (Shanghai Second Polytechnic University)

  • Jiaofei Zhong

    (University of Texas at Dallas)

Abstract

This paper studies a two-person cooperative game in which a set of jobs has to be processed jointly by two people. Each of them has a single machine and his processing cost is defined as the minimum value of the maximum latency of his negotiably assigned jobs. The objective is to maximize the multiplication of their rational positive cooperative profits. In the case where all jobs have the same processing time, if they have a common due date, the problem is polynomial-time solvable; if due dates can be different, there exits an optimal schedule in which the jobs assigned to each person are scheduled in Earlier Due Date first (EDD) order and a polynomial-time dynamic programming is further proposed. In the case where processing times can be different, the NP-completeness of this problem is proved, and a pseudo-polynomial-time dynamic programming algorithm is developed.

Suggested Citation

  • Yanhong Gu & Jing Fan & Guochun Tang & Jiaofei Zhong, 2013. "Maximum latency scheduling problem on two-person cooperative games," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 71-81, July.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9434-y
    DOI: 10.1007/s10878-011-9434-y
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    References listed on IDEAS

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    8. Lahiri, S., 2003. "Axiomatic characterization of the Nash and Kalai-Smorodinsky solutions for discrete bargaining problems," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 14(3), pages 207-220.
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    Cited by:

    1. Lili Liu & Guochun Tang & Baoqiang Fan & Xingpeng Wang, 2015. "Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 938-948, November.
    2. Ling Gai & Jiandong Ji, 2019. "An integrated method to solve the healthcare facility layout problem under area constraints," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 95-113, January.
    3. Peng Liu & Xiaoli Wang, 2017. "Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date," Journal of Optimization, Hindawi, vol. 2017, pages 1-7, April.
    4. Xi Chen & Zhiping Fan & Zhiwu Li & Xueliang Han & Xiao Zhang & Haochen Jia, 2015. "A two-stage method for member selection of emergency medical service," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 871-891, November.

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    Keywords

    Scheduling; Game; Cooperation; Profit;
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