A collaborative planning framework combining the Lagrangian Relaxation method and Genetic Algorithms 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 sub-problems based on the separability of it. Genetic Algorithms was incorporated into Lagrangian Relaxation method 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 schema 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 in terms of both performance and robustness.
Relationship-specific investment and hold-up problems in supply chains: theory and experiments