A Lagrangian based solution algorithm for a build-to-order supply chain network design problem

This paper presents a Lagrangian based solution algorithm for the network design problem in a build-to-order (BTO) supply chain. The problem is to determine where to locate the distribution centers and to which distribution center or plant the retailers are assigned. The demand is assumed to be lead-time-dependent, and the balance between lead time and logistics costs is considered. Integer programming models are developed to formulate the problem. As it is difficult to obtain precisely optimal solution to this kind of problems, a Lagrangian based solution algorithm is developed to obtain near optimal solution. Problems involving hundreds of distribution centers and retailers are used to test the algorithm. Computational results show that the Lagrangian based algorithm can present very good solutions to all the examples in short CPU time. Scenario analyses and some managerial insights are reported.