Sharif University of Technology Scientia Iranica 1026-3098 25 3 2018 06 01 A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem 1750 1767 4447 10.24200/sci.2017.4447 EN Davood Shishebori Department of Industrial Engineering, Yazd University, P.C.1684613114, Yazd, Iran Abolghasem Yousefi Babadi School of Industrial and systems Engineering, University of Tehran, Tehran, Iran Zohre Noormohammadzadeh Department of Industrial Engineering, Yazd University, P.C.1684613114, Yazd, Iran Journal Article 2016 05 26 This study considers a multi-objective combined budget constrained facility location/network design problem (FL/NDP) in which the 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 the network reliability versus uncertainty, an efficient 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, fixed cost of road/link utilization as well as minimizing the total penalties of uncovered demand nodes. Then, in order to consider of several system uncertainty, the proposed model is changed to a fuzzy robust model by suitable approaches. An efficient Sub-gradient based Lagrangian relaxation algorithm is applied. In addition, a practical example is studied. At 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 of practical factors (e.g., several uncertainties, system disruptions, and customer satisfaction) in modelling of the problem can lead to significant improvement of the system yield and subsequently more efficient utilization of the established network.  <br /> <strong> </strong> https://scientiairanica.sharif.edu/article_4447_dc93de4ed08928a49de89ce6c8694e1b.pdf