Annals of Operations Research

, Volume 222, Issue 1, pp 361–387 | Cite as

Value-at-Risk model for hazardous material transportation

  • Yingying Kang
  • Rajan Batta
  • Changhyun Kwon


This paper introduces a Value-at-Risk (VaR) model to generate route choices for a hazmat shipment based on a specified risk confidence level. VaR is a threshold value such that the probability of the loss exceeding the VaR value is less than a given probability level. The objective is to determine a route which minimizes the likelihood that the risk will be greater than a set threshold. Several properties of the VaR model are established. An exact solution procedure is proposed and tested to solve the single-trip problem. To test the applicability of the approach, routes obtained from the VaR model are compared with those obtained from other hazmat objectives, on a numerical example as well as a hazmat routing scenario derived from the Albany district of New York State. Depending on the choice of the confidence level, the VaR model gives different paths from which we conclude that the route choice is a function of the level of risk tolerance of the decision-maker. Further refinements of the VaR model are also discussed.


Hazardous materials transportation Value-at-Risk Social risk mitigation 



This research was partially supported by National Science Foundation grant CMMI-1068585. The authors are grateful to Iakovos Toumazis for his help in data management and numerical computation.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Norfolk Southern CorporationAtlantaUSA
  2. 2.Department of Industrial & Systems EngineeringUniversity at Buffalo, the State University of New YorkBuffaloUSA

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