The Generalized Vehicle Routing Problem (GVRP) is an extension of the classical Vehicle Routing Problem (VRP), in which we are looking for an optimal set of delivery or collection routes from a given depot to a number of customers divided into predefined, mutually exclusive, and exhaustive clusters, visiting exactly one customer from each cluster and fulfilling the capacity restrictions. This paper deals with a more generic version of the GVRP, introduced recently and called Selective Vehicle Routing Problem (SVRP). This problem generalizes the GVRP in the sense that the customers are divided into clusters, but they may belong to one or more clusters. The aim of this work is to describe a novel mixed integer programming based mathematical model of the SVRP. To validate the consistency of the novel mathematical model, a comparison between the proposed model and the existing models from literature is performed, on the existing benchmark instances for SVRP and on a set of additional benchmark instances used in the case of GVRP and adapted for SVRP. The proposed model showed better results against the existing models.

In this article, we address a variant of the vehicle routing problem which occurs in real-life applications, called the clustered vehicle routing problem. The clustered vehicle routing problem (CluVRP) looks for an optimal collection of routes, with respect to cost minimization, for a fleet of vehicles, fulfilling all customers’ requirements which have a particular structure being divided into clusters, the capacity constraints of the vehicles and with the additional constraint that all the customers belonging to the same cluster must be visited consecutively before leaving the cluster. We propose a novel approach for solving the problem using a decomposition-based method which splits the CluVRP into two easier subproblems. The results of the computational experiments on three sets of benchmark instances from the literature show that our approach is competitive in comparison with the known solution approaches published to date.