A mixed integer mathematical model and a heuristic approach for two echelon location routing problem with simultaneous pickup and delivery

This study considers Two Echelon Location Routing Problem with Simultaneous Pickup and Delivery (2E/LRP-SPD). In a two-echelon distribution network consisting of factories, warehouses and customers, the aim is to determine which facilities will be opened in which candidate regions and routing activities to be carried out among them. Routing activities include distributing and collecting activities. While distributing activities are performed from primary facilities (factory) to secondary facilities (depots) and secondary facilities to customers, collecting activities are done from customers to the secondary facilities and from secondary facilities to primary facilities. We propose a two-index node based mixed integer programming formulation for the 2E-LRPSPD. As the problem is in NP-Hard problem class, a constructive heuristic algorithm based on Clarke-Wright algorithm is developed to solve medium- and large- size problems. The performance of the heuristic approach is investigated on test instances derived from literature. Computational results show that heuristic algorithm gives good quality solutions for medium- and large-size instances in a very short computation time. Thus, the contribution of this study to the literature is to present an efficient mathematical model for solving small-size problems and to develop a constructive heuristic algorithm that produces very fast and high-quality solutions for medium and large-size problems.