Overview of fuzzy vehicle routing problems

Introduction. Various algorithms for solving fuzzy vehicle routing problems are considered. The work objective was to study modern methods for the optimal solution to fuzzy, random and rough vehicle routing problems. Materials and Methods. The paper reviews fuzzy vehicle routing problems, existing methods and approaches to their solution. The most effective features of some approaches to solving fuzzy vehicle routing problems considering their specificity, are highlighted. Results. The Fuzzy Vehicle Routing Problem (FVRP) occurs whenever the routing data is vague, unclear, or ambiguous. In many cases, these fuzzy elements can better reflect reality. However, it is very difficult to use Vehicle Routing Problem (VRP) solving algorithms to solve FVRP since several fundamental properties of deterministic problems are no longer fulfilled in FVRP. Therefore, it is required to introduce new models and algorithms of fuzzy programming to solve such problems. Thus, the use of methods of the theory of fuzzy sets will provide successful simulation of the problems containing elements of uncertainty and subjectivity. Discussion and conclusions. As a result of reviewing various methods and approaches to solving vehicle routing problems, it is concluded that the development and study of new solutions come into sharp focus of researchers nowadays, but the degree of elaboration of various options varies. Methods for the optimal solution of FVRP are limited, in general, to some single fuzzy variable. There is a very limited number of papers that consider a large number of fuzzy variables