Reliable Facility Location-Allocation Optimization Model under the Risk of Disruptions

In the classic models of facility location, it is assumed that the selected facilities always work based on the schedule while, in the real world, facilities are always exposed to disruption risk and sometimes these disruptions have long-term effects on the supply chain network and cause a lot of problems. In this paper, a mixed integer programing (MIP) model presented in order to determine how to serve the customers at the time of disruption in distribution centers in a two-echelon supply chain, including distribution centers and customers. This model selects potential places that minimize traditionally supply chain costs and also the transportation cost after distribution centers disruptions. In fact, the model tries to choose the distribution centers facilities with lowest cost and highest reliability and also allocate them to customers. The problem divided into two sub-problems using Lagrangian relaxation approach. By examining sub-problems optimal conditions, a heuristic solution is used for the first sub-problem and a genetic algorithm is used for the second sub-problem to solve large-scale problems. Finally, numerical examples are presented to examine the performance and efficiency of the proposed model and approach.