Bi-Objective Vehicle Routing for Hazardous Materials Transportation with No Vehicles Travelling in Echelon

As a by-product of industrial development, large quantities of hazardous materials are shipped in the transportation network every day. The risk of transporting hazardous materials is an important consideration in transportation planning. Vehicle routing models in previous studies simultaneously minimized the transportation cost and the total risk. However, simply evaluating the total risk of a fleet as a whole does not consider each individual vehicle's risk. Even if the total risk is low, the risk of a specific vehicle may still be very high. In addition, the situation of several vehicles of a logistics company shipping hazardous materials and travelling on the same road together, called vehicles travelling in echelon, may cause a chain of incidents. This situation has been ignored in previous studies. In this paper, a bi-objective vehicle routing model for hazardous materials transportation with no vehicles travelling in echelon is developed, simultaneously minimizing the maximum risk of each vehicle and the transportation cost. A two-stage exact algorithm is developed based on the \varepsilon -constraint method with several improvements to solve the proposed problem. An approximation approach is proposed for this two-stage algorithm for large-scale problems. Furthermore, the approximation ratio and time complexity of this approximation algorithm are analyzed. Computational experiments with randomly generated instances are reported, and several managerial insights are derived from the sensitivity analysis.