A new fuzzy version of the risk-constrained cash-in-transit vehicle routing problem

Abstract

This paper considers the Risk-constrained Cash-in-Transit Vehicle Routing Problem (RCTVRP), a variant of the vehicle routing problem which takes into account risk factors of the routes. In this problem, the risk constraints are set by using a risk threshold T on each route and thus, the routes with risk larger than T are forbidden. The main idea of this paper is to use the possibility of being robbed along each route, instead of just allowing solutions with routes that satisfy the risk constraints. We develop a new fuzzy version of the RCTVRP, called FRCTVRP, which considers the value of the risk index of each route and the solutions with lower values of risk indexes on their routes are considered as better. In order to achieve that, fuzzy numbers are incorporated into the new formulation. Moreover, two mixed integer program formulations of the FRCTVRP are developed in the paper. The introduced FRCTVRP is compared with the classical RCTVRP from the literature on an adequate example and the advantage of the newly proposed FRCTVRP is demonstrated. Computational experiments are performed and the comparison given in the paper shows that our approach leads to safer routes.