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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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.
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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