modeling and solving the multi-depot vehicle routing problem with time window by considering the flexible end depot in each route

this paper considers the multi-depot vehicle routing problem with time window in which each vehicle starts from a depot and there is no need to return to its primary depot after serving customers. the mathematical model which is developed by new approach aims to minimizing the transportation cost including the travelled distance, the latest and the earliest arrival time penalties. furthermore, in order to reduce the problem searching space, a novel ga clustering method is developed. finally, experiments are run on number problems of varying depots and time window, and customer sizes. the method is compared to two other clustering techniques, fuzzy c means (fcm) and k-means algorithm. experimental results show the robustness and effectiveness of the proposed algorithm.