Fuzzy goal programming facility location network design problem under uncertainty: A Lagrangian relaxation and Robust Optimization approaches

The combined facility location and network design problem is an important practical problem for locating public and private facilities. In this paper, we consider a multi objective combined facility location/network design problem which considers system uncertainty. This problem has a number of applications, many of which fall into the category of service systems, such as regional planning and locating schools, health care service centers and airline networks. Moreover, an investment budget constraint is raised on facility locating and link constructing. Therefore, this model determines the optimal locations of new facilities, link roads that should be constructed and also demand nodes covered by these facilities and link roads. The proposed model is formulated based on an efficient robust optimization approach to protect the network against uncertainty. Then, in order to consider of several system uncertainty, the proposed model is changed to a fuzzy robust model by suitable approaches. An efficient Lagrangian relaxation algorithm is applied.