A multi objective FLND problem under uncertain environment using robust optimization: A heuristic approach and case study

In this paper, a robust multi objective mixed integer linear programming model is proposed for a robust facility location network design problem, which takes uncertain parameters (including demand and transfer costs) into the account. The proposed model simultaneously minimizes the total operating costs and maximizes the total coverage. Moreover, an investment budget constraint is raised on facility location and link construction. 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. Then, the proposed model is robust by suitable approaches. An efficient multi objective approach, based on Lp-metrics- is proposed and tested for several test problems. A practical case study, based on an integrated distribution system, is presented in detail to illustrate the application of the proposed mathematical model. Finally, a sensitivity analysis is done to provide an insight into the behavior of the proposed model in response to changes of key parameters of the problem.