Nash equilibria for the multi-agent project scheduling problem with controllable processing times
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This paper considers a project scheduling environment in which the activities of the project network are partitioned among a set of agents. Activity durations are controllable, i.e., every agent is allowed to shorten the duration of its activities, incurring a crashing cost. If the project makespan is reduced with respect to its normal value, a reward is offered to the agents and each agent receives a given ratio of the total reward. Agents want to maximize their profit. Assuming a complete knowledge of the agents’ parameters and of the activity network, this problem is modeled as a non-cooperative game and Nash equilibria are analyzed. We characterize Nash equilibria in terms of the existence of certain types of cuts on the project network. We show that finding one Nash equilibrium is easy, while finding a Nash strategy that minimizes the project makespan is NP-hard in the strong sense. The particular case where each activity belongs to a different agent is also studied and some polynomial-time algorithms are proposed for this case.
KeywordsMulti-agent project scheduling Nash equilibria Flow networks
This work was supported by the ANR Project No. 08-BLAN-0331-02 named “ROBOCOOP.” The authors wish to acknowledge two anonymous reviewers for their remarks that significantly helped improving the paper.
- Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network flows. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
- Demeulemeester, E. L., & Herroelen, W. S. (2002). Project scheduling—a research handbook. Dordrecht: Kluwer Academic Publishers.Google Scholar
- Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W. H. Freeman & Co.Google Scholar
- Knotts, G., Dror, M., & Hartman, B. C. (2000). Agent-based project scheduling. IIE Transactions, 32(5), 387–401.Google Scholar
- Lau, J. S. K., Huang, G. Q., Mak, K. L., & Liang, L. (2005b). Distributed project scheduling with information sharing in supply theoretical analysis and computational study. International Journal of Production Research, 43(23), 4899–4927. Google Scholar
- Li, Z., & Zhou, H. (2012). Coordination mechanism of economic lot and delivery scheduling problem. Industrial Engineering Journal, 15, 18–22.Google Scholar
- Phillips, S., & Dessouky, M. I. (1977). Solving the project time/cost tradeoff problem using the minimal cut concept. Management Science, 24(4), 393–400.Google Scholar
- Wang, L., Zhan, D., Nie, L., & Xu, X. (2011). Research framework for decentralized multi-project scheduling problem. In 2011 International Conference on Information Science and Technology, ICIST 2011, pp. 802–806.Google Scholar