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In this paper we consider a multiobjective job shop scheduling problem. The machines are subject to availability constraints that are due to preventive maintenance, machine breakdowns or tool replacement. Two optimization criteria were considered; the makespan for the jobs and the total cost for the maintenance activities. The job shop scheduling problem without considering the availability constraints is known to be NP-Hard. Because of the complexity of the problem, we develop a two-phase genetic algorithm based heuristic to solve the addressed problem. A set of pareto optimal solutions is obtained in the first phase containing relatively large number of solutions. This makes difficult the choice of the most suitable solution. For this reason the second phase will filter the obtained set so as to reduce its size. Performance of the proposed heuristic is evaluated through computational experiments on the benchmark of Muth & Thomson mt06 of 6×6 and 10 different sizes benchmarks of Lawrence. The results show that the heuristic gives solutions close to those obtained in the classic job shop scheduling problem.