location and allocation of a distribution system considering disruption in mobile warehouses and backup facilities

in this paper, a facility location problem of distribution systems, as one of the important and strategic issues in supply chain management, has been studied in a three-level supply chain under a stochastic condition. for this purpose, a two-stage mathematic model has been proposed for the location-allocation problem of distribution systems with regard to backup facilities for disrupting warehouse storage facilities in the three-level supply chain that minimizes the sum of the costs. in the first stage, locating the mobile warehouse of distribution systems and transferring the products between manufactures and mobile warehouses have been decided and in the second stage, meeting customer demands with regard to disrupting mobile warehouses and backup facilities have been also decided. in addition, disruption in warehouses is considered as different scenarios for overcoming computational time in large dimensions. moreover, a lagrangian relaxation solution framework to reduce solution time is used. finally, numerical examples are solved with gams software and then the objective function of the problem is compared with the objective function of a lagrangian relaxation solution to show the effectiveness of the proposed model.