A collaborative planning framework based on the Lagrangian Relaxation method is developed to coordinate and optimize the production planning of the independent partners linked by material flows in multiple tier supply chains. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP) for supply chains. Model MLCLSP was Lagrangian relaxed and decomposed into facility-separable subproblems based on the separability of it. Surrogate gradient algorithm was used to update Lagrangian multipliers, which coordinated decentralized decisions of the facilities in supply chains. Production planning of independent partners could be appropriately coordinated and optimized by this framework without intruding their decision authorities and private information. This collaborative planning scheme was applied to a large set problem in supply chain production planning. Experimental results show that the proposed coordination mechanism and procedure come close to optimal results as obtained by central coordination.