A hazardous materials vehicle routing problem with time-dependent arc capacity

The transportation of vehicles fully loaded with hazardous materials on road segments with high population density, or the simultaneous presence of multiple hazardous materials vehicles on the same road, significantly increases transportation risk. To ensure the safe operation of vehicles carrying hazardous materials on the road, we develop a mathematical framework based on the time-dependent vehicle routing problem with time windows (TDVRPTW). This framework treats each road segment as an independent entity and incorporates the variation of its external environment over time. Specifically, it integrates the arc capacity with time-dependent attributes, forming the time-dependent arc capacity (TDAC). The TDAC controls the risks in each road segment by implementing restrictions on the total quantity of hazardous materials allowed to enter. The restriction is based on the specific external environments during different time periods of the day. To address these time-dependent factors in path searching, we develop an algorithm called the Time-Dependent Variant of Dijkstra’s Algorithm with Time-Dependent Weight. We then integrate this algorithm into a bi-objective tabu search approach to solve the TDVRPTW. We utilized the augmented $\varepsilon$-constraint method to solve small-scale problems and compared the results with those obtained from heuristic algorithms. Subsequently, by conducting computational experiments on road networks of various scales, we validate the efficiency of our heuristic algorithm. The results show that our method can achieve a more reasonable distribution of risks, enable staggered utilization of roads, and effectively control the overall risk of the system and the risk of each road in the network at a relatively low level. Moreover, these benefits are achieved without significantly increasing the total cost.