Two novel sweep-based heuristics for the vehicle routing problem

The vehicle routing problem (VRP) is a well-known complex problem and widely used in supply chains. The objective is to construct an optimal set of routes serving a number of customers under some constraints. The purpose of this study is to present two novel heuristics based on a new density distance which uses the polar coordinates of the sweep algorithm and the customer demand. The proposed algorithms use the ratio between the customer demands and the polar coordinates as ordering criteria. The proposed heuristics are based on three steps. In the first step, a giant tour is constructed by using two new ordering criteria. Next, the split procedure is applied to get feasible routes subject to the vehicles' capacities. Finally, each route of the constructed solution is improved by the application of the nearest neighbour heuristic. The results of the experiment indicate that the proposed heuristics are encouraging.