Multi-depot vehicle routing problem for hazardous materials transportation: A fuzzy bilevel programming

Due to enormous demand and potential threat to public, hazardous materials transportation has been tremendously investigated in recent years. However, there are few studies focusing on multi-depot vehicle routing problem for hazardous materials transportation. In this study, we develop a fuzzy bilevel programming model for minimizing the total expected transportation risk when delivering products of hazardous materials to customers from multiple depots. The upper level formulation allocates customers to depots under the constraints of depot capacities and customer demands, while the lower level determines the optimal path for each group of depots and customers. For obtaining the optimal solution to the proposed model, four fuzzy simulation-based heuristic algorithms are designed. Illustrative examples demonstrate the effectiveness of the proposed model and the four heuristics.