Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints

Network design models are extensively used to represent a wide range of planning and operation management issues in transportation, telecommunications, logistics and production-distribution. In a very general sense, the problem consists of designing a network by selecting links to connect a set of nodes and to determine the amount of flow on each link such that the demand of each node for a number of commodities is satisfied. The objective is to minimize the total cost of establishing the links and flows. This basic variant is usually referred to as the uncapacitated network design problem. The problem has extensions that arise when additional restrictions are incorporated, such as imposing capacity limits on the amount of demand that may be transported on the links (referred to as the capacitated network design problem). Interested readers on the problem may consult the surveys by Magnanti and Wong [7] and Minoux [8]. Network design formulation provide a good modelling framework for service network design problems, usually at the strategic or the tactical level, for which Crainic [3] gives an overview and a classification of formulations.