In many real-life applications, it can be often found that multiple agents compete on the usage of a common processing resource in different application environments and different methodological fields, such as artificial intelligence, decision theory, operations research, etc. Moreover, scheduling with multiple agents is relatively unexplored. Based on this observation, this paper attempts to study a single-machine scheduling problem where the objective is to minimize the total tardiness of the first agent with the constraint that no tardy job is allowed for the second agent. In this study, we provide a branch-and-bound algorithm and a genetic algorithm for the optimal and near-optimal solutions. We also report a computational experiment to evaluate the impact of the parameters involving with proposed problem simulation settings.

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