Routing-Loading Balance Heuristic Algorithms for a Capacitated Vehicle Routing Problem

Vehicle routing problems (VRPs) is an outstanding topic in the domain of logistics. Besides the theoretical interest of VRP, its importance arises mainly from its significant applications. A prevalent variation of the VRP called the capacitated VRP (CVRP) assumes that vehicle capacity is limited and that the sum of demands in a route served by a vehicle should not surpass its capacity. The classical VRPs and CVRPs are classified in the category of NP-hard problems. Therefore heuristic approaches are used in order to obtain approximate solutions to real life problems, the size of which are beyond the adequacy of exact solution algorithms. The CVRP investigated in this paper consider the optimality objective that find a set of vehicle tours in order to cover all the demands at maximum uniform vehicle utilization, simultaneously taking into account a smooth vehicle loading throughout the vehicle fleet. The principle procedure of the algorithm presented in this paper is a suitable neighborhood search scheme that seeks to decrease most of the deviation between the maximum and the minimum vehicle travel times, as well as the corresponding deviation of the loading volume of the vehicles in the fleet. The paper ends with a detailed small numerical example