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Two game-based solution concepts for a two-agent scheduling problem

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Abstract

In the current research papers on multi-agent (multi-person) scheduling, a person’s objective function is always considered as a cost function on scheduling, whereas a cooperative profit function is defined to serve as his objective one in this paper. In the two-person scheduling problem addressed in this paper, the two persons jointly order a common operational time interval of a single machine. Each person needs to process a set of his own jobs in that time window. The same objective function of each person still relies on the sequence of all the jobs of both persons since each part of the function is determined by some given parameters except one part assumed to be a given multiple of the total completion time of his own jobs. The two persons have to negotiate a job sequence and determine the (related) final solution on cooperative profit allocation. Such a two-person scheduling problem is essentially a cooperative game. An algorithm is designed to yield the cooperative-profit-based Pareto efficient solution set acting as the first game-based solution concept in this paper. The parallelized version of the algorithm is also developed. The second game-based solution concept is the Shapley value appropriate for the above cooperative-game situation on two-person scheduling. Several instances are presented and analyzed to reveal the necessity to employ the two solution concepts together.

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Acknowledgments

The authors are grateful to the editor and the anonymous referees for their constructive comments and suggestions. This paper was supported by the Natural Science Foundation of China (Grant No. 61273220).

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Authors and Affiliations

  1. Intelligent Computational Science Institute, College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Bing Zhao & Yanhong Gu

  2. College of Computer Science & Software Engineering, Shenzhen University, Shenzhen, 518060, China

    Yuan Ruan

  3. The Logistics Institute—Asia Pacific, National University of Singapore, Singapore, 117574, Singapore

    Quanle Chen

Authors
  1. Bing Zhao
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  2. Yanhong Gu
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  3. Yuan Ruan
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  4. Quanle Chen
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Correspondence to Yanhong Gu.

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Zhao, B., Gu, Y., Ruan, Y. et al. Two game-based solution concepts for a two-agent scheduling problem. Cluster Comput 19, 769–781 (2016). https://doi.org/10.1007/s10586-016-0557-x

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  • DOI: https://doi.org/10.1007/s10586-016-0557-x

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