Fuzzy Stochastic Capacitated Vehicle Routing Problem and Its Applications

This paper considers Capacitated Vehicle Routing Problem (CVRP) in an imprecise and random environment. The deterministic version of the problem deals with finding a set of routes in such a way that the demand of all the customers present in the network are satisfied and the cost incurred in performing these operations comes out to be a minimum. In practical life situations, problems are not always defined in crisp form. Phenomena like randomness and impreciseness are quite natural to arise in real life. This work presents CVRP in such a mixed environment, such type of CVRP may be called as Fuzzy Stochastic Capacitated Vehicle Routing Problem. In this work, the demands of the customers are assumed to be stochastic and are revealed only when a vehicle arrives at the customer location. Moreover, the edge weights represent time required to traverse the edge and hence are both imprecise and random in nature. Factors like traffic conditions, weather conditions, are responsible for the random nature of the edge weights and the varying speed of the vehicle is responsible for impreciseness. Thus, the work presents CVRP with stochastic demands and stochastic and imprecise travel times. In this paper, an expectation-based approach has been used to deal with the randomness of edge weights. A two-stage model is used to solve the problem where the first stage corresponds to finding an optimal tour and recourse actions are planned in the second stage. A procedure based on Branch and Bound algorithm has been used to find minimum cost route. A small numerical example is presented to explain the working of the method proposed and the proposed solution approach is further tested on modified fuzzy versions of some benchmarks datasets.