In this study, we propose a distributed cooperative scheduling method, and apply the method into a machine maintenance scheduling problem in re-entrant production systems. As one of the distributed cooperative scheduling methods, we focus on Lagrangian decomposition and coordination (LDC) method, and formulate the machine maintenance scheduling problem with LDC so as to improve computational efficiency by decomposing an original scheduling problem into several sub-problems. The derived solutions by solving the decomposed dual problem are converted into feasible solutions with a heuristic procedure applied in this study. The proposed approach regards maintenance as job with starting and finishing time constraints, so that product and maintenance schedule can realize proper maintenance operations without losing productivity. We show the effectiveness of the proposed method in several simulation experiments.