A heuristic algorithm for the constrained location - routing problem

The logistics system of a firm deals with purchasing materials (acquisition logistics), controls work in process in each production phase (production logistics system), through the distribution management, it controls the flow of the products delivered to the customer (distributive logistics), defines the backtracking of a discarded, disused or damaged product, to reemploy its parts or materials (reverse logistics). The structures displaced within the logistics network must guarantee an opportune level of service and the cutback of logistics costs. Transport system performance are, therefore, of primary importance, as well as the location of the distribution centers and products distribution issues. In literature they are present accurate mathematical models and effective solution techniques to face location, allocation and distribution problems. The topic is still of extreme interest because of the increasing structural complexity of the models due to the constraints imposed by the “real systems” representation. Integrated location routing models are used to solve the facility location problem (FLP) and the vehicle routing problem (VRP) simultaneously so to reflect the interactions between the two decisions. In this paper, particularly, a possible approach (the TSP- VRP heuristic) will be proposed to optimize the routing phase in a Location-Routing Problem (LRP). Results are compared with those obtainable turning to other commonly adopted procedures.