The Hazardous Materials Transportation Network Design Problem

The production and transportation of hazardous materials (hazmat) plays an important role in industrial development. Although the probability of hazmat transportation accidents is low, the vast majority of transporting hazmat and inadequate supervision by the government causes frequent hazmat transportation accidents, which arouse close national attention in China. The total annual hazmat transport volume reached about400million tons in China. Among them, about95%hazmat need to be transported from one place to another and road transportation accounts for approximately82%. What differentiates hazmat transport from the transportation of other materials is the risk associated with an accidental release of hazmat during transportation. Due to the nature of the hazmat, in case accidents happen, it may cause unpredictable harm to people, property and the environment. Thus, mitigation of hazmat transportation risk is an increasingly significant challenge and is a serious concern for the government of China. One way to mitigate hazmat transportation risk for government is to close certain roads to hazmat vehicles since it cannot force specific routes for individual shipments.All the models studied in the field of hazmat transportation network design are based on the deterministic risk value on each arc. However, the hazmat transportation accidents are recognized as low probability-high consequence events and the risk is a significant ingredient which separates hazmat transportation problems from other transportation problems. It is not easy to estimate the risk on each arc exactly, since it depends on many unpredictable factors. There are several elements to influence the risk on each arc, such as human error, weather conditions, transport mode, vehicle type and road conditions involving people living around the road, road intersections, highway ramps and bridges where accidents happen frequently. The risk assessment is a basic research branch for other research fields in hazmat transportation, involving qualitative or quantitative risk assessment. The qualitative risk assessment deals with the identification of possible accidents in the absence of data and the quantitative risk assessment uses historical accident frequencies and consequences to calculate the numerical assessment of risks. However, the past empirical data is not very reliable. There is no agreement on accident probabilities and conflicting numbers of edge risk reported by different researchers could induce different results. Furthermore, weather conditions, public perceived risk and hot spots, such as road intersection, highway ramps and bridges, may cause unpredictable severe accidents, making the risk of road segments uncertain. When the risk changes on the road segments, the prior optimal network might not be an optimal network any more, then the network lacks of robustness. To design a robust hazmat transportation network is reasonable and necessary.We consider the problem of designing a transport network for the hazardous materials where the government can decide which road segments have to be closed to hazardous materials so as to minimize the overall risk of the shipments; the carriers choose the routes on the designated network to minimize their route costs. For the hazmat transport network design problem, it was shown that there exists an optimal path of risk0is NP-hard. This implies that the problem does not admit any approximation, neither any FPT algorithm, unless P==NP. The hazardous transportation network design problem faces significant uncertainty in conflicting numbers of edge risk reported by different researchers and many influencing edge risk factors which induced different result. In this paper, we use a robust optimization to model the problem as a robust bi-level integer programming formulation under edge risk uncertainty. We provide a heuristic approach that always finds a robustness and stable hazmat network. In the end of the paper, we test on a random instance to illustrate the efficient of our model and algorithm. We test the above algorithm on the network for Guangdong province China, which has21nodes and30edges. We adopt four different classified hazmat data on this network, including explosive solid product, flammable gas, toxic gas and corrosive substances.In this paper, we also consider a problem of transportation network design for the hazardous materials where the government considers both public risk and transportation cost. We model the problem as a bi-objective bi-level network transportation formulation, in which the upper decision model allows decision makers to trade off risk and cost, and the lower decision model optimize the transportation risk with risk equity. Let a e [0,1] be a parameter that indicates the relative importance of the risk and cost objectives for the government. At the end of the paper, we give the efficient algorithm to solve the model.