Abstract
In this paper, we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we characterize the set of Pareto-optimal schedules in terms of size and computational complexity. We then address the problem from the single-agent point-of-view, that is, we consider the problem of deciding how to submit one agent’s tasks only taking into account its own objective function against the other agent, the opponent. In this regard, we consider two different settings depending on the information available to the agents: In one setting, the considered agent knows in advance all information about the submission sequence of the opponent; and in the second setting (as in minimax strategies in game theory), the agent has no information on the opponent strategy and wants to devise a strategy that minimizes its solution cost in the worst possible case. Finally, we assess the performance of some classical single-agent sequencing rules in the two-agent setting.
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Notes
Note that this assumption is without loss of generality: The case in which the two agents tasks sets have different cardinality can be easily addressed by considering dummy tasks with 0 processing times and weights.
Since anyway \(i\) would be placed before \(j\) in block \(D_{k(j)}\), these arguments hold also for \(s=k(j)\).
The result was probably proved elsewhere, but we are not aware of any reference.
References
Agnetis, A., Billaut, J.-C., Gawiejnowicz, S., Pacciarelli, D., & Soukhal, A. (2014). Multiagent scheduling: Models and algorithms. Berlin: Springer.
Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with two competing agents. Operations Research, 52(2), 229–242.
Agnetis, A., Nicosia, G., Pacifici, A., & Pferschy, U. (2013). Two agents competing for a shared machine. In Proceedings of the 3rd international conference on algorithmic decision theory (ADT 2013), Lecture notes in computer science 8176, pp. 1–14, Springer: Berlin.
Agnetis, A., Pacciarelli, D., & Pacifici, A. (2007). Combinatorial models for multi-agent scheduling problems, in multiprocessor scheduling: Theory and applications. Vienna, Austria: I-Tech Education and Publishing.
Agnetis, A., De Pascale, G., & Pranzo, M. (2009). Computing the Nash solution for scheduling bargaining problems. International Journal of Operational Research, 6(1), 54–69.
Arbib, C., Smriglio, S., & Servilio, M. (2004). A competitive scheduling problem and its relevance to UMTS channel assignment. Networks, 44(2), 132–141.
Baker, K., & Smith, J. C. (2003). A multiple criterion model for machine scheduling. Journal of Scheduling, 6(1), 7–16.
Cohen, J., Cordeiro, D., Trystram, D., & Wagner, F. (2011). Multi-organization scheduling approximation algorithms. Concurrency and computation: Practice and experience, 23(17), 2220–2234.
Darmann, A., Nicosia, G., Pferschy, U., & Schauer, J. (2014). The subset sum game. European Journal of Operational Research, 233(3), 539–549.
Ding, G., & Sun, S. (2010). Single-machine scheduling problems with two agents competing for makespan (pp. 244–255). Lecture notes in computer science, 6328, Berlin: Springer.
Garey, M. R., Tarjan, R. E., & Wilfong, G. T. (1988). One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research, 13(2), 330–348.
Hall, N. G., & Liu, Z. (2013). Market good flexibility in capacity auctions. Production and Operations Management, 22(2), 459–472.
Huynh, Tuong N., Soukhal, A., & Billaut, J.-C. (2012). Single-machine multi-agent scheduling problems with a global objective function. Journal of Scheduling, 15(1), 311–321.
Jayasudha, A. R., & Purusothaman, T. (2012). Job scheduling model with job sequencing and prioritizing strategy in grid computing. International Journal of Computer Applications, 46(24), 29–32.
Leung, J. Y.-T., Dror, M., & Young, G. H. (2001). A note on an open-end bin packing problem. Journal of Scheduling, 4, 201–207.
Marini, C., Nicosia, G., Pacifici, A., & Pferschy, U. (2013). Strategies in competing subset selection. Annals of Operations Research, 207(1), 181–200.
Nicosia, G., Pacifici, A., & Pferschy, U. (2009). Subset weight maximization with two competing agents. In Proceedings of algorithmic decision theory: ADT 2009, Lecture notes in computer science 5783, pp. 74–85, Berlin: Springer.
Nicosia, G., Pacifici, A., & Pferschy, U. (2011). Competitive subset selection with two agents. Discrete Applied Mathematics, 159(16), 1865–1877.
Nicosia, G., Pacifici, A., & Pferschy, U. (2014). Scheduling the tasks of two agents with a central selection mechanism, submitted. available as: Optimization Online 2014–02-4222.
Pessan, C., Bouquard, J.-L., & Neron, E. (2008). An unrelated parallel machines model for an industrial production resetting problem. European Journal of Industrial Engineering, 2, 153–171.
Soomer, M. J., & Franx, G. J. (2008). Scheduling aircraft landings using airlines’ preferences. Mathematical Programming, 190, 277–291.
T’Kindt, V., & Billaut, J.-C. (2006). Multicriteria scheduling. Theory, models and algorithms. Berlin: Springer.
Wellman, M. P., Walsh, W. E., Wurman, P. R., & MacKie-Mason, J. K. (2001). Auction protocols for decentralized scheduling. Games and Economic Behavior, 35(1/2), 271–303.
Ye, D., & Zhang, G. (2012). Coordination mechanisms for selfish parallel jobs scheduling. In M. Agrawal, et al. (Eds.), 9th Annual conference on theory and applications of models of computation, 2012 (pp. 225–236). Lecture notes in computer science 7287. Berlin:Springer.
Acknowledgments
This work was supported by the Austrian Science Fund (FWF): [P 23829-N13] and by the Italian Ministry MIUR Project PRIN 2009XN4ZRR_002.
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Agnetis, A., Nicosia, G., Pacifici, A. et al. Scheduling two agent task chains with a central selection mechanism. J Sched 18, 243–261 (2015). https://doi.org/10.1007/s10951-014-0414-9
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DOI: https://doi.org/10.1007/s10951-014-0414-9