Bi-Objective Vehicle Routing for Hazardous Materials Transportation With Actual Load Dependent Risks and Considering the Risk of Each Vehicle

Abstract

As a consequence of industrial development, large quantities of hazardous materials are shipped everyday. Most related studies consider the risks as fixed weights on edges. However, the loads of the vehicles are important factors about the risks. Thus, considering the risks as fixed parameters cannot reflect actual practice. In addition, the vehicle routing models in previous studies simultaneously minimize the total transportation cost and the total risk. However, simply considering the total risk of a fleet as a whole cannot evaluate each vehicle's risk. Although the total risk is low, the risk of a specific vehicle may still be very high. In this paper, the actual load dependent risk is introduced, and a corresponding bi-objective vehicle routing model for hazardous materials transportation is developed, minimizing the maximum risk of vehicles and the total transportation cost simultaneously. An exact algorithm is developed based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon $</tex-math></inline-formula> -constraint method with several improvements. For large-scale problems, an approximation approach is proposed. Computational experiments on a series of instances are reported and several managerial insights are derived from the sensitivity analysis.