Future Directions

Specific extensions related to each of the three contributions were elaborated in the respective chapters i.e. Chapters 2-4. In the following, we point out other directions for the future research.

5.2.1. Time-dependent Stochastic Network

Routing of hazmat shipments in the networks that have time-dependent stochastic attributes (such as travel times) is an interesting and challenging operations research problem that has not yet been studied adequately. The results from fixed travel time models may produce schedules which lead to longer journeys, and hence give rise to further congestion and associated costs. Hence, in situations where travel times are uncertain and the probability distributions vary with the time of day, the transport network should be modeled as a stochastic time-dependent network. In such a network, the link attributes (such as travel times, incident probabilities, and population exposure) are represented as random variables with a priori probability distributions that vary with time (Erkut et al., 2007).

In deterministic networks, there is only one minimum time path connecting a shipper to a receiver. However, in stochastic time-dependent networks, multiple paths may have positive probability of having the least time, as the arc times are stochastic. Therefore, a set of non-dominated solutions can be estimated. The major concern to solve the routing problems in stochastic time-dependent networks is the collection and processing of the data required to assess the probability distribution used as input to the model. Time-

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dependent stochastic networks have been studied during the past two decades, but only very few of them consider hazmat transportation (e.g., Bowler and Mahmassani, 1998; Miller-Hooks and Mahmassani, 1998). Among these few papers, none of them take multiple objectives or multiple modes into account. In addition, they are all about local route planning, rather than global routing. Unlike the local routing, which focuses on a single commodity and a single origin-destination route plan, the global routing problem involves multi-commodity and multiple origin-destination routing decisions. In the future, we can study the global routing of hazmat freights in a time-dependent stochastic network.

5.2.2. Terrorist Attack

Another future research direction is to consider the potential for a terrorist attack on a hazmat vehicle. Traditionally, traffic accidents or human error were regarded as factors affecting risk. However, the hazmat vehicles could be the desirable targets for terrorists, specifically because of the corresponding exposure risks. This fact should be considered when modeling the risk in the problems similar to ours in Chapters 3 and 4. To assess the risk of terrorist attack involving hazardous materials, the tiered approach used to designate varying levels of highway/rail security-sensitive materials2, frequency of shipment of hazmat freights and the consequence of attack should be considered (Reniers and Zamparini, 2012).

2 _{Security-sensitive materials have legitimate industrial use but can be exploited by terrorists and be}

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In addition to the risk assessment, the routing of hazmat freight could be affected by probability of terrorist attack. Besides the minimization of cost, minimizing the probability of a successful terrorist attack could also be regarded as objective functions. Applying game theory to model the interaction between a carrier and a terrorist would help the carrier make decisions of which routes to use with what frequencies with regard to threat of the terrorism. Reilly et al. (2012) is one of the few studies which model the possible role of a terrorist when designing a network of hazmat. They developed a Stackelberg game in which the government acts as a leader to maximize the carriers’ payoff and limit the terrorist’s payoff by restricting specific facilities. The main drawback of the developed model is that only one carrier is considered. The model can be extended to address multiple carriers, each with several origins and destinations. Furthermore, it would be interesting to study a similar problem in an intermodal network with multiple stakeholders. Unlike the road network, where the government has the options of restricting specific facilities or closing the links, the rail-truck intermodal networks have other important stakeholders (i.e., private carrier companies) which are important to be coordinated with the government when making restricting decisions.

5.2.3. Risk Equity

Finally, equity in distribution of risk should be taken into account when designing hazmat management strategies acceptable to the public. Since carriers’ decisions are usually made without considering the general setting, it may happen that some parts of the transportation network are overloaded with hazmat freights. This may cause considerable

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increase of accident rates in those parts, resulting in inequity on distribution of the risk. In traditional approaches, different paths would be generated to alternate the route among them and hence distribute the risk. Recently, bi-level optimization is used to tackle risk equity. Since the government cannot impose specific routes on carriers, policies could be adopted to regulate the use of the network links and therefore promote equity in the spatial distribution of risk. Although several studies have focused on risk equity (e.g. List and Mirchandani, 1991; Current and Ratick, 1995; Kang et al., 2014), very few of them have presented a bi-level formulation (e.g. Bianco et al., 2009), which is a more appropriate methodology to study an uncooperative situation where different authorities act as multiple decision makers. All available models consider only one mode of transportation; however risk equity in an intermodal network is different from a single mode network. Different studies showed that equity can be enhanced using alternate routes for a shipment. Though this is possible in a road network, the scarcity of railroad in different areas does not present many routing options. In a rail network, train make-up, i.e., the composition of the train, is the major factor affecting the risk equity. For a certain amount of demand, the use of fewer trains would lead to an increase in the exposure zone while reducing the number of times people close to the tracks are exposed. Verma and Verter (2007) showed that, when the train passes through a populated area, with a uniform population density, the exposure will spread over large number of people, and hence improve the equity. Studying the risk equity in a rail truck network of hazmat would be a significant contribution.

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