An Efficient Imperialist Competitive Algorithm for Solving Location Routing Problem in the Multi-Level Supply Chain Under Fuzzy and Probabilistic Condition

In the industrial world today, manufacturing units are trying to locate your requirements and the depot vehicle routing in order to transport the goods for reduce your cost. Needless to mention that the location of the warehouse is effective for vehicle routing. Therefore, in this paper, a mathematical programming model to optimize the storage location and vehicle routing are presented. The objective function of the model is minimizing the total cost associated with the transportation and storage of rental fee. Limitations of the model include vehicle capacity, the maximum distance traveled by vehicles and etc. In addition, labor costs, such as salaries, rent, warehouses, rental vehicles and etc. Approach to model the real world has been considered.Also, since each location and routing issues alone are a NP-hard problem, then location routing problem can be combined problem and It requires the use of meta- heuristic algorithms to solve.