Hierarchical design of an integrated production and 2-echelon distribution system

This study uses the method of Lagrangean relaxation in the hierarchical design of an integrated model of production–distribution functions in a 2-echelon system. A mixed integer mathematical model is developed with a centralized planning perspective to address production and distribution decisions simultaneously. In order to solve the resulting large-scale problem, the Lagrangean relaxation is used to decouple the imbedded distribution and production sub-problems, and subgradient optimization is implemented to coordinate the information flow between these in a hierarchical manner. This corresponds to a decentralized organizational design where a central agent coordinates the information exchange between the distribution and production organizational units. A forward heuristic designed to solve the distribution subproblem is shown to provide good solutions. Hierarchical interdependency is incorporated into the Lagrangean heuristic such that distribution decisions are placed in the top level to restrict the solution of the production subproblem in the lower level.