Spectral risk measure minimization in hazardous materials transportation

Abstract

Due to catastrophic consequences of potential accidents in hazardous materials (hazmat) transportation, a risk-averse approach for routing is necessary. In this article, we consider spectral risk measures, for risk-averse hazmat routing, which overcome challenges posed in the existing approaches such as conditional value-at-risk. In spectral risk measures, one can define the spectrum function precisely to reflect the decision maker’s risk preference. We show that spectral risk measures can provide a unified routing framework for popular existing hazmat routing methods based on expected risk, maximum risk, and conditional value-at-risk. We first consider a special class of spectral risk measures, for which the spectrum function is represented as a step function. We develop a mixed-integer linear programming model in hazmat routing to minimize these special spectral risk measures and propose an efficient search algorithm to solve the problem. For general classes of spectral risk measures, we suggest approximation methods and path-based approaches. We propose an optimization procedure to approximate general spectrum functions using a step function. We illustrate the usage of spectral risk measures and the proposed computational approaches using data from real road networks.

Keywords:

• Hazardous materials transportation; risk management; spectral risk; coherent risk measures

Notes

1 The path is $106\to 1\to 2\to 7\to 17\to 19\to 28\to 34\to 39\to 47\to 55\to 52\to 53\to 48\to 51\to 63\to 67\to 71$, and the details about the Ravenna network (Bonvicini and Spadoni, 2008; Erkut and Gzara, 2008) are introduced in Section 6.

Additional information

Funding

This research was supported by the National Science Foundation grant CMMI-1558359.

Notes on contributors

Liu Su

Liu Su received a B.S. degree in industrial engineering from Huazhong University of Science and Technology, Wuhan, China, in 2013 and an M.S. degree from the Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA, USA, in 2015. She is currently working toward a Ph.D. degree with the Department of Industrial and Management Systems Engineering, University of South Florida, Tampa, FL, USA. Her research interests include optimization theories and applications in transportation and power systems.

Longsheng Sun

Longsheng Sun is a senior analyst — statistics and operations research at United Airlines. He obtained his Ph.D. in industrial and systems engineering at the State University of New York at Buffalo. His research interests include discrete optimization, machine learning, robust optimization, and network optimization methods, with applications to transportation, revenue management, logistics and supply chain management problems.

Mark Karwan

Mark Karwan, Praxair Professor in Operations Research and SUNY Distinguished Teaching Professor, has served 42 years in the Department of Industrial and Systems Engineering, University at Buffalo. Thirty-four Ph.D. students have been guided in modeling and algorithmic development, mathematical programming, and multiple criteria decision making. His application areas include logistics, production planning, hazardous waste routing, military path planning and analytics.

Changhyun Kwon

Changhyun Kwon is an associate professor in industrial and management systems engineering at the University of South Florida. His research interests include transportation systems analysis and service operations problems. He received a Ph.D. in industrial engineering in 2008 and an M.S. in industrial engineering and operations research in 2005, both from the Pennsylvania State University. He also received a B.S. in mechanical engineering from KAIST in 2000. He received an NSF CAREER award in 2014. Before he joined the University of South Florida, he was with the University at Buffalo, where he received the UB Exceptional Scholar: Young Investigator Award in 2015.