green vehicle routing problem with safety and social concerns

Over the two last decades, distribution companies have been aware of the importance of paying simultaneous attention to all economical, environmental, social, and safety aspects of a distribution system for success in the global market. the economic issue is often used in case of the vehicle routing problem (vrp) literature, while the environmental, the safety and the social concerns constitute less proportion of studies. the green vehicle routing problem (gvrp) is one of the recent variants of the vrp, dealing with environmental aspects of distribution systems. in this paper, two developed mixed integer programming models are presented for the gvrp with social and safety concerns. moreover, a genetic algorithm (ga) is developed to deal efficiently with the large-sized problem . different numerical analyses have been performed to validate the presented algorithm in comparison to exact solutions and to investigate the influence of several key factors such as the effect of increasing the cost of safety aspect on route balancing and customer's waiting time. the results confirm that the proposed algorithm performs well and has more social and safety benefits, including more balanced tours and fewer customers' waiting time than those of the classic gvrp.