A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem

This study considers a multi-objective combined budget constrained Facility Location/Network Design Problem (FL/NDP), in which system uncertainty is considered. The most obvious practical examples of the problem are territorial designing and locating of academies, airline networks, and medical service centers. In order to assure network reliability versus uncertainty, an ecient robust optimization approach is applied to model the proposed problem. The formulation is minimizing the total expected costs, including transshipment costs, Facility Location (FL) costs, and xed cost of road/link utilization as well as minimizing the total penalties of uncovered demand nodes. Then, in order to consider several system uncertainties, the proposed model is changed to a fuzzy robust model by suitable approaches. An ecient sub-gradient based Lagrangian relaxation algorithm is applied. In addition, a practical example is studied. In the following, a series of experiments, including several test problems, is designed and solved to evaluate of the performance of the algorithm. The obtained results emphasize that considering practical factors (e.g. several uncertainties, system disruptions, and customer satisfaction) in modelling of the problem can lead to signicant improvement of the system yield and, subsequently, more ecient utilization of the established network.