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Conventional methods for simultaneous production scheduling and routing problem have hierarchical decomposition scheme where production scheduling problem and routing problem are separately solved due to computational complexity. We propose a novel decomposition method with cut generation. The entire problem is decomposed into a upper level subproblem for production scheduling and task assignment problem and a lower level subproblem for collision-free routing of multiple AGVs. The novel idea of the proposed method is the upper level subproblem which is solved by using Lagrangian relaxation technique incorporating cuts generated from a solution of the lower level subproblem. The algorithm solves successively the upper level problem and the lower level problem until a near-optimal solution for original problem is derived. The effectiveness of the proposed method is investigated from numerical experiments.