International Journal of Industrial Engineering & Production Management

 During the last three decades, the integrated optimization approach to logistics systems has become one of the most important aspects of the supply chain optimization. This approach simultaneously considers the interdependence of the location of the facilities, suppliers/customers allocation to the facilities, the structure of transportation routes, and inventory planning and control. Location-routing problem is one of the most important classes of location problems for considering this approach. In this problem, the number and location of facilities, size of the transportation fleet, and the route structures are to be found with respect to the location and characteristics of suppliers and customers. In this study, a mathematical model, an efficient and fast heuristic algorithm, an effective metaheuristic algorithm based on simulated annealing, and a new lower bound for the two-echelon location-routing problem with vehicle fleet capacity and maximum route length constraints are presented. At the end, the computational results show the efficiency of the proposed algorithms using the proposed obtained lower bound.