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A coordination mechanism for a scheduling game with parallel-batching machines

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Abstract

In this paper we consider the scheduling problem with parallel-batching machines from a game theoretic perspective. There are m parallel-batching machines each of which can handle up to b jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch, and all the jobs in a batch start and complete at the same time. There are n jobs. Each job is owned by a rational and selfish agent and its individual cost is the completion time of its job. The social cost is the largest completion time over all jobs, the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of pure Nash Equilibria and offer upper and lower bounds on the price of anarchy of the coordination mechanism. We show that the mechanism has a price of anarchy no more than \(2-\frac{2}{3b}-\frac{1}{3\max \{m,b\}}\).

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Acknowledgments

This research was supported in part by the National Natural Science Foundation of China under Grant Numbers 11201439 and 11271341. This work was also supported in part by the Shandong Provincial Natural Science Foundation, China, under Grant Number ZR2012AQ12 and by the Doctoral Fund of Ministry of Education of China (20120132120001).

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Authors and Affiliations

  1. School of Mathematical Science, Ocean University of China, Qingdao, 266071, Shandong, People’s Republic of China

    Q. Q. Nong, G. Q. Fan & Q. Z. Fang

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  1. Q. Q. Nong
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  2. G. Q. Fan
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  3. Q. Z. Fang
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Correspondence to Q. Q. Nong.

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Nong, Q.Q., Fan, G.Q. & Fang, Q.Z. A coordination mechanism for a scheduling game with parallel-batching machines. J Comb Optim 33, 567–579 (2017). https://doi.org/10.1007/s10878-015-9980-9

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  • DOI: https://doi.org/10.1007/s10878-015-9980-9

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