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We extend the hazardous-materials (hazmat) network design problem to account for the time-dependent road closure as a policy tool to reduce hazmat transport risk by altering carriers' departure times and route choices.We formulate the time-dependent network design problem using an alternative-based model with each alternative representing a combined path and departure-time choice.We also present an extended model that can not only account for consecutive time-based road closure policies but also allow stopping at the intermediate nodes of the network in the routing/scheduling decisions of the carriers. Heuristic algorithms based on column generation and label setting are presented. To illustrate the advantages that can be gained through the use of our methodology, we present results from numerical experiments based on a transportation network from Buffalo, New York. To investigate the impact of the extensions, we consider three versions of the problem by gradually refining the model. We show that under consideration of extensions, the design policies are more applicable and effective. [ABSTRACT FROM AUTHOR]

Despite significant advances in risk management, the routing of hazardous materials (hazmat) has relied on relatively simplistic methods. In this paper, we apply an advanced risk measure, called conditional value-at-risk (CVaR), for routing hazmat trucks. CVaR offers a flexible, risk-averse, and computationally tractable routing method that is appropriate for hazmat accident mitigation strategies. The two important data types in hazmat transportation are accident probabilities and accident consequences, both of which are subject to many ambiguous factors. In addition, historical data are usually insufficient to construct a probability distribution of accident probabilities and consequences. This motivates our development of a new robust optimization approach for considering the worst-case CVaR (WCVaR) under data uncertainty. We study important axioms to ensure that both the CVaR and WCVaR risk measures are coherent and appropriate in the context of hazmat transportation. We also devise a computational method for WCVaR and demonstrate the proposed WCVaR concept with a case study in a realistic road network. [ABSTRACT FROM AUTHOR]

We study robust network design problems for hazardous materials transportation considering risk uncertainty. Risk uncertainty is considered in two ways: (1) uncertainty on each link for each shipment, and (2) uncertainty on each link across all shipments. We extend an existing heuristic framework to solve these two robust network design problems and propose a Lagrangian relaxation heuristic to solve subproblems within the framework. We present our computational experiences and illustrate general insights based on real networks. [ABSTRACT FROM AUTHOR]

In this paper, we study a novel toll setting policy to regulate hazardous material (hazmat) transportation, where the regulator (e.g., a government authority) aims at minimizing not only the network total risk but also at spreading the risk in an equitable way over a given road network. The idea is to use a toll setting policy to discourage carriers transporting hazmat from overloading portions of the network with the consequent increase of the risk exposure of the population involved. Specifically, we assume that the toll paid by a carrier on a network link depends on the usage of that link by all carriers. Therefore the route choices of each carrier depend on the other carrier's choices, and the tolls deter the carriers from using links with a high total risk. The resulting model is a mathematical programming with equilibrium constraints (MPEC) problem, where the inner problem is a Nash equilibrium problem (game) having as players the carriers, each one wishing to minimize his or her travel cost (including tolls); the outer problem is addressed by the government authority, whose aim is finding the link tolls that induce the carriers to choose route plans that minimize both the network total risk and the maximum link total risk among the network links (to address risk equity). To guarantee the stability of the solution, we study conditions for the existence and uniqueness of the Nash equilibrium, and propose a local search heuristic for the MPEC problem. Computational results are carried out on a real road network, comparing the performance of our toll setting policy with the toll setting approach proposed in the literature. [ABSTRACT FROM AUTHOR]

The people living and working around the roads used for hazardous material (hazmat) shipments face the risk of suffering undesirable consequences of an accident. The main responsibility to mitigate the hazmat transport risk at a population zone belongs to the government agency with jurisdiction over that region. One of the common policy tools is to close certain road links to vehicles carrying hazmats. In effect, the road network available to dangerous goods carriers can be determined by the regulator. The transport risk in the region, however, is determined by the carriers' routing decisions over the available road network. Thus, the regulator needs to make the road closure decisions so that the total risk resulting from the carriers' route choices is minimized. We provide a path-based formulation for this network design problem. Alternative solutions can be generated by varying the routing options included in the model for each shipment. Each solution corresponds to a certain compromise between the two parties in terms of transport risk and economic viability. The proposed framework can be used for identifying mutually agreeable hazmat transport policies. We present two applications of the methodology to illustrate the insights that can be gained through its use: The first application focuses on hazmat shipments through the highway network of Western Ontario, Canada, whereas the second application studies the problem in a much larger geographical region that covers the provinces of Ontario and Quebec. [ABSTRACT FROM AUTHOR]

Dangerous-goods shipments remain regulated despite the widespread deregulation of the transportation industry. This is mainly due to the societal and environmental risks associated with these shipments. One of the common tools used by governments in mitigating transport risk is to close certain roads to vehicles carrying hazardous materials. In effect, the road network available to dangerous goods carriers can be determined by the government. The associated transport risk, however, is determined by the carriers' route choices. We provide a bilevel programming formulation for this network design problem. Our approach is unique in terms of its focus on the nature of the relationship between the regulator and carriers. We present an application of our methodology in Western Ontario, Canada. [ABSTRACT FROM AUTHOR]

We consider the strategic level routing problem of hazardous materials in marine waters over a multicommodity network with multiple origins-destinations. The problem is motivated by the fact that selecting optimal routes by each origin-destination pair or by each type of material is myopic and may result in overloading certain links of the transportation network and, consequently, in poor overall system performance. We employ a network flow model, instead of the traditional shortest path formulation, to capture the multicommodity, multiple origin-destination nature of the problem. An efficient two-phase solution approach is proposed. The proposed solution methodology is illustrated through a single hazmat problem followed by a large scale case study of the marine transportation system of oil products in the Gulf of Mexico. [ABSTRACT FROM AUTHOR]

This paper derives six objectives for routing hazardous material by viewing shipments as a sequence of independent Bernoulli trials. An example that compares these objectives is presented. Suitable approximations toward the use of these objectives in an optimization framework are provided. The paper also discusses the objectives from the viewpoint of their use to make actual hazardous material routing decisions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of determining a path that maximizes a multi-attribute, non-order-preserving value function. The motivating application is the determination of a most preferred path for transporting hazardous materials based on transportation cost and risk to population. A sub-path of an optimal path may not be optimal for a non-order-preserving value function, implying that a traditional application of dynamic programming may intentionally or unintentionally produce sub-optimal paths. We consider two approximation procedures for two general cases, the q = 0 case and the q > 0 case, where q is the number of required intermediate stops between origin and destination. The first approximation procedure involves applying dynamic programming as if a sub-path of an optimal path were always optimal. The second approximation procedure involves determining a linear order-preserving criterion that approximates the non-order-preserving value function and then applying dynamic programming. We use the best-first search algorithm BU* to determine optimal routes for both the q = 0 and q > 0 cases. We examine the frequency and magnitude of the resulting sub-optimalities for a multi-attribute value model based on a six-county road network that includes Cleveland, Ohio. Numerical results show that if one of the two approximations is used, significant sub-optimalities can occur over a wide range of decision maker preferences. Both approximations can produce sub-optimality error magnitudes of over 50%. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development and analysis of a mathematical model for determining a route that attempts to reduce the risk of low probability-high consequence accidents related with the transportation of hazardous materials. The approach adopted considers trade-offs between the conditional expectation of a catastrophic outcome given that an accident has occurred, and more traditional measures of risk dealing with the expected value of the consequence and the accident probability on a selected path. More specifically, the problem we address involves finding a path that minimizes the conditional expectation objective value, subject to the expected value of the consequence being lesser than or equal to a specified value v, and the probability of an accident on the path being also constrained to be no more than some value η. The values v and η are user-prescribed and could be prompted by the solution to the shortest path problems that minimize the respective corresponding linear risk functions. The proposed model is a discrete, fractional programming problem that is solved using a specialized branch-and-bound approach. A numerical example is provided for the sake of illustration, and some computational experience on randomly generated test cases is provided to study the effort required to solve this problem in different instances. The model is also tested using realistic data associated with a case concerned with routing hazardous materials through the roadways of Bethlehem, Pennsylvania. Data acquisition as well as algorithmic computational issues are discussed. [ABSTRACT FROM AUTHOR]

The economic loss associated with the involvement of a hazardous materials truck in an accident can be very high. Although the immediate costs are usually borne by an insurer, the carrier would incur an increase in its future insurance costs as a result. Thus, a hazardous materials carrier can benefit from considering its long-term insurance costs in routing the required shipments. In this paper, we introduce the hazardous materials routing problem under insurance costs. We present a solution methodology that facilitates evaluation of alternative routing policies. The proposed methodology involves solution of a manageable number of shortest path problems in determining the most appropriate route(s). We argue that, for each shipment, the route to be taken by the truck should be determined on the basis of the expected increase in insurance costs due to a possible accident as well as the cost of transportation. [ABSTRACT FROM AUTHOR]

This paper considers integrated location and routing models for minimizing the expected number of hazardous material transport accidents. Two different routing policies are considered: (1) most reliable route planning and (2) multiple routing with random selection. Path reliability measurements are used to derive the expected number of accidents over a given planning horizon, where reliability refers to the probability of completing a journey without accident. Corresponding to the two routing policies, two location models are introduced: the reliable 1-median and a location framework for considering multiple routes. Based on realistic assumptions for assigning accident probabilities to segments created when an edge location is considered, vertex optimality results for both problems are obtained. An example to illustrate reliable routing and location in Massachusetts is provided. [ABSTRACT FROM AUTHOR]

Recognition of time-varying patterns of accident rates and exposure parameters can be used to improve routing and scheduling decisions for hazardous materials shipments. An integrated routing/scheduling approach can be used to reduce overall risk, and find preferred solutions in a multiobjective context. We describe a method for performing an integrated routing/scheduling analysis, and illustrate its use in a case study. We also construct estimates of the "value of information" for incorporation of this time-dependent data. [ABSTRACT FROM AUTHOR]

This paper discusses the variance-constrained shortest path problem. This problem can be used to model any application in which the travel costs on a link are not deterministic, but follow a distribution that has possible correlation with travel cost on other links. Exact solution methods are proposed, and results are reported from computational experiments on data sets derived from a real-life routine scenario involving the transportation of liquefied-gas hazardous materials. [ABSTRACT FROM AUTHOR]

Commercially available tracking systems based on advanced communications and computing technology allow a dispatcher of hazardous material transports to monitor the movement of vehicles on a transportation network in real time. When unexpected events occur, a dispatcher working with this new technology can identify the regions surrounding the transportation network that are affected by these events and determine safe and cost-effective routes for the vehicles that plan to drive through those regions. Four decision models for rerouting hazardous material vehicles in real-time have been assessed in an experimental setting. The first model supports a dispatcher in finding alternative routes (visually), while the second model adds to the display, for each vehicle, an alternative route based on a conservative heuristic. The other two models are based on an ordinal preference and a numerical utility structure to support the dispatcher in determining the impact of the events on transportation safety and costs. The models were embedded into four decision support systems that use multimedia technology to simulate the dispatchers workstations. These systems were then used in an experiment at the dispatching school in Wil, Switzerland, with 32 experienced dispatchers and truck drivers to assess efficiency and accuracy of the four models. The results show that assessing risks and costs with the ordinal preference structure, prior to making routing decisions, is significantly more efficient and accurate than searching directly for new routes. Using a numerical scale for safety and cost assessment was disliked by the subjects and led to inferior results. [ABSTRACT FROM AUTHOR]

Models are formulated and computed to assess the risks of hazardous materials releases in train derailments in terms of: the probability of any number of fatalities in an accident, the probability of any total number of fatalities from all the accidents in a year, and the frequency of accidents which result in any given number of fatalities. These functions are evaluated using data bases and analytical methods which provide estimates of exposure levels (traffic volumes, track conditions and population densities), spill occurrence and spill size probabilities, and fatal spill impacts (the size of the lethal area in any given accident scenario). Despite the sparsity of historical data, this methodology enables us to express the potential for catastrophic occurrences in quantitative terms, to compare these numbers with estimates of other risks, and to examine the effects of selective variations in the model inputs. [ABSTRACT FROM AUTHOR]

The transport of hazardous materials is an important strategic and tactical decision problem. Risks associated with this activity make transport planning difficult. Although most existing analytical approaches for hazardous materials transport account for risk, there is no agreement among researchers on how to model the associated risks. This paper provides an overview of the prevailing models, and addresses the question "Does it matter how we quantify transport risk?" Our empirical analysis on the U.S. road network suggests that different risk models usually select different "optimal" paths for a hazmat shipment between a given origin-destination pair. Furthermore, the optimal path for one model could perform very poorly under another model. This suggests that researchers and practitioners must pay considerable attention to the modeling of risks in hazardous materials transport. [ABSTRACT FROM AUTHOR]

This paper considers two new decision-making problems in the context of transporting hazardous materials (HM). These problems are motivated by the fact that many practical situations only have a finite number of shipments of HM to be made and that shipments are likely to be suspended after a threshold number of accidents. Both problems are nonlinear, constrained shortest path problems. Exact solution methods are proposed and computational results are reported for the case where the threshold number of accidents is one. Extension of the methodology for higher values of the threshold number of accidents is also outlined. [ABSTRACT FROM AUTHOR]

In this paper, we develop and analyze a model to generate an equitable set of routes for hazardous material shipments. The objective is to determine a set of routes that will minimize the total risk of travel and spread the risk equitably among the zones of the geographical region in which the transportation network is embedded, when several trips are necessary from origin to destination. An integer programming formulation for the problem is proposed. We develop and test a heuristic that repeatedly solves single-trip problems: a Lagrangian dual approach with a gap-closing procedure is used to optimally solve single-trip problems. We report a sampling of our computational experience, based on a real-life routing scenario in the Albany district of New York State. Our findings indicate that one can achieve a high degree of equity by modestly increasing the total risk and by embarking on different routes to evenly spread the risk among the zones. Furthermore, it appears that our heuristic procedure is excellent in terms of computational requirements as well as solution quality. We also suggest some directions for future research. [ABSTRACT FROM AUTHOR]

This paper considers the problem of determining optimal paths for routing an undesirable vehicle on a network embedded on an Euclidean plane. A typical application is the transporting of hazardous materials. Demand points, or population centers, are discretely distributed at nodes and continuously distributed on straight-line links of the network. The objective is to find, without incorporating the probability of accidental leakage of hazardous material, a path that minimizes the weighted sum of lengths over which this vehicle is within a threshold distance lambda of population centers. By appropriately redefining link lengths, we can use a shortest-path algorithm to solve the problem. Special properties of the objective function allow us to efficiently calculate the modified link lengths. We discuss the properties of the optimal routing strategy and the objective value, and offer an economic interpretation of the case when lambda varies. Operating within the framework of risk analysis, we integrate the probability of accidental release of hazardous material into our basic model. The routing objective becomes the minimization of expected damage, where accidental leakage of hazardous materials can inflict damage within a neighborhood lambda of the accident site. We also discuss our computational experience in using the model. [ABSTRACT FROM AUTHOR]

The article presents information about the contents of the August 1997 issue of the journal "Transportation Science." According to the author, the goal of this focused issue is to present the readers of "Transportation Science" with a collection of papers representing the state-of-the-art in this area as it is seen from an operations research perspective. In his opinion, problems in this area are multiple objective complicated due to many factors: models are data-hungry, the underlying problems are of a combinatorial nature, accounting for risks is not a straightforward matter, and there are multiple objectives. According to the author, the article "Location and Reliable Routing of Hazmats," published in this issue considers integrated location and routing models for minimizing the expected number of hazmat transport accidents. Two different routing policies are considered: most reliable route planning, and multiple routing with random selection. Path reliability measurements are used to derive the expected number of accidents over a given planning horizon, where reliability refers to the probability of completing a journey without accident.