Integrated Optimization Model to Manage Risk of Transporting Hazardous Materials on Railroad Networks

ment of the risk posed by these materials requires an understanding of how different approaches may reduce risk and their relative cost-effectiveness both alone and in combination. There are various approaches to hazardous materials transportation risk reduction. A variety of operations research techniques have been developed and applied to consider each approach individually, including consideration of hazardous materials transportation routing (3–6), improving transportation packaging (7–9), upgrading track infrastructure (10), and managing the operating speed of hazardous materials trains (11). Saat and Barkan developed a preliminary comparative analysis of the effect of tank car safety design versus alternative routing (12) and infrastructure improvements (13). However, the authors are unaware of research that considers and compares more than one approach to risk reduction simultaneously. Such comparison is important to objectively evaluate different approaches, possible interactive effects, and relative cost-effectiveness and to determine optimal strategies. Each risk reduction strategy has characteristic benefit and cost functions. A release event is typically conditioned on a series of earlier events—a train accident or derailment, hazardous material car involvement, and hazardous material car damage and release. Each event has its own probability distribution, which in turn affects the result of the risk equation. Lowering any of the terms in this equation will reduce risk, but the form and extent of the reduction associated with each term varies. Different risk reduction strategies affect the terms differently. For example, packaging enhancement involving tank car design improvement reduces the conditional probability of release from a tank car involved in an accident but does not reduce accident rates. Conversely, upgrading track infrastructure offers reduction in accident rates but does not affect the conditional probability of release from a tank car involved in an accident provided that operating speed remains the same. However, there are interactive effects among the terms that affect the cost–benefit analysis, which complicates comparison among different risk reduction strategies. The multiplicative form of the risk equation means that the benefit associated with a particular risk reduction strategy is affected by changes to others terms in the equation. Thus improving packaging reduces the benefit derived from improving infrastructure, and vice versa, but the cost associated with each of these strategies is unchanged. Consequently, implementing a risk reduction strategy may reduce the cost-effectiveness of other strategies. This study presents an integrated risk management framework model to provide a means of choosing the most effective set of risk mitigation strategies for a particular rail network. The model is first formulated using nonlinear programming (NLP) and converted into Integrated Optimization Model to Manage Risk of Transporting Hazardous Materials on Railroad Networks