Multiple-agent scheduling has attracted growing interest in recent years. Most of previous research focused on the single-machine environment. However, some situations make this assumption impractical, since some jobs require to be executed on different machines. In this work, we address a two-machine job shop scheduling problem with two competing agents. The main objective is to minimize the makespan of the first agent subject to an upper bound on the makespan of the second agent. In some situation we will consider the total completion time as an objective function for the second agent. We investigate the complexity of several problems. Then, we focus on the two- machine job shop problem with two agents and two operations. To solve this problem optimally for small instance, we provide a mathematical model and a branch and bound algorithm. In addition, we propose an heuristic with different priority lists, and a genetic algorithm to find near optimal solutions. Finally, we present analysis of computational experiments.



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