Vehicle routing optimization with soft time windows in a fuzzy random environment

This paper is concerned with a vehicle routing problem with soft time windows (VRPSTW) in a fuzzy random environment. Two objectives are considered: (1) minimize the total travel cost and (2) maximize the average satisfaction level of all customers. After setting up the model for the VRPSTW in a fuzzy random environment, the fuzzy random expected value concept is used to deal with the constraints and its equivalent crisp model is derived. The global-local-neighbor particle swarm optimization with exchangeable particles (GLNPSO-ep) is employed to solve the equivalent crisp model. A case study is also presented to illustrate the effectiveness of the proposed approach.