Analysis of mathematical formulations of capacitated vehicle routing problem and methods for their solution

Vehicle Routing Problem (VRP) is one of the most widely known questions in a class of combinatorial optimization problems. It is concerned with the optimal design of routes to be used by a fleet of vehicles to serve a set of customers. In this study we analyze Capacitated Vehicle Routing Problem (CVRP) - a subcase of VRP, where the vehicles have a limited capacity. CVRP is mostly aimed at savings in the global transportation costs. The problem is NP-hard, therefore heuristic algorithms which provide near-optimal polynomial-time solutions will be considered instead of the exact ones. The aim of this article is to make a survey on mathematical formulations of CVRP and on methods for solving each type of this problem. The first part presents a general information about the problem and restrictions of this work. In the second part, the classical mathematical formulations of CVRP are described. In the third part, a classification of most popular subcases of CVRP is given, including description of additional constraints with their math formulations. This section also includes most perspective methods that can be applied for solving special types of CVRP. The forth part contains an important note about the most powerful algorithm LKH-3. Finally, the fourth part consists of table with solving techniques for each subproblem and of scheme with basic problems of the CVRP class and their interconnections.