To the classification of vehicles routing problems

The essence of the problems considered consists in developing routes for a group of heterogeneous vehicles based in a specific place or places (depot) that have to deliver goods to customers according to their volume of orders. The classic vehicle routing problem belongs to combinatorial optimization problems, which can be represented as a graph with the set of vertices representing both the depot and the delivery point, i.e. customers, and the set of edges corresponding to the paths. In this problem, the following data are given: matrix of edges weights between vertices, determined by the value/length of paths; the number of vehicles involved in the delivery of the goods; volumes of goods to be delivered to customers at each delivery point. The topicality of the vehicle routing problem has led to the emergence of numerous studies conducted over the last decades and relevant publications. While composing the list of scientific publications cited in the article, the authors did not aim to provide a historical perspective on the study of vehicle routing problem (it is quite fully reflected in the majority of works), but preferred the publications of recent years that show the current state of research. Most real-world vehicle routing problems have additional constraints that give rise to a whole range of new problem formulations. The paper presents a number of classes of vehicle routing problems. The main limitation is the capacity, and the criterion is the total cost of transportation. In routing problems with time constraints or “time windows”, minimizing the total cost of transportation is combined with minimizing the number of vehicles involved and the overall waiting time for vehicle customers. Minimizing the cost of transportation and the size of the park of the involved vehicles can be required even if these vehicles leave from several depots, and both the start and the end of the route may be located not in fixed, but in alternative, in particular, dynamic depots. Beside the above mentioned the following tasks are considered: routing problems for return and delivery of goods, routing with two-dimensional restrictions on vehicle loading, maximization of savings on goods transportation, routing with different modes of transport, periodic routing with random data, routing with the possibility of loading, routing with predefined deadlines. For each problem type additional restrictions that differ from the classical problem are introduced