Modeling and Solving the Vehicle Routing Problem with Multiple Fuzzy Time Windows

Abstract

Considering that the customers could accept service in multiple time periods and the fuzziness of service time periods, this paper deals with the multiple time windows as fuzzy variables and quantifies the customer satisfaction level according to the membership function of the beginning time to be served, on the basis of the given acceptable satisfaction level, the vehicle routing model with multiple fuzzy time windows is constructed in order to minimize the transportation cost and number of vehicles and maximize the satisfaction level. Then according to the model characteristics, we use the punishment factors to deal with the constraints and apply particle swarm operations to solve the proposed problems. The experimental results show the effectiveness of proposed algorithm in solving the vehicle routing problems with multiple fuzzy time windows. Comparing the calculated results with the hard time window model results, it is found that our proposed model is more effective to reduce the cost of distribution.