Collaborative planning in supply chains based on Lagrangian relaxation and genetic algorithm

Optimization of collaborative planning among partners across various supply chains was studied. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP) model for supply chains. Based on separable structures of the model, MLCLSP was decomposed into facility-separable sub problems by Lagrangian relaxation technology. Genetic algorithm was incorporated into Lagrangian relaxation method to update the Lagrangian multipliers so as to coordinate decentralized decisions of the facilities. The production planning of independent partners could be coordinated and optimized by this framework without interfering their decision authority and private information. Simulation experiments showed that the proposed mechanism and algorithm came close to optimal results as obtained by central coordination in terms of both performance and robustness.