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 collisionfree 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.