A possibilistic programming approach for the vehicle routing problem with time windows

This paper considers the vehicle routing problem with time windows where the uncertainties of travel times are modeled with possibility distributions. A possibilistic programming model is designed for the problem. Furthermore, an ant colony system algorithm is developed to solve the proposed model. Necessity measure is used to gain knowledge about the feasibility of generated solutions when they are realized. Finally, numerical examples are given to show the effectiveness and usefulness of the algorithm.