Project Description

The objective of this research is to investigate how conditional value-at-risk (CVaR) models mitigate risk in hazardous materials (hazmat) transportation on time-dependent vehicular networks. Accidents involving hazmat bring significant damage to our society and often require long-term efforts to clear. Routing of hazmat transportation must consider accident probabilities and accident consequences that depend on the hazmat types and route choices. This research project proposes new methods for mitigating risk in hazmat transportation, based on CVaR measure. While CVaR models are popularly used in financial portfolio optimization problems, its application in hazmat is new. Recently, the PI proposed value-at-risk (VaR) models for routing hazmat transportation considering equity between areas. The VaR models are shown to be flexible and general routing models for hazmat transportation, and be solved efficiently. This research project will extend the previous research by considering CVaR for hazmat transportation on time-dependent networks under data uncertainty.

The risk along the same route can become significantly different depending on the time of travel. For example, we do not want hazmat trucks traveling on very congested roads, even though they may be the safest route in uncongested time periods. To consider this important issue of time-dependent risk factors in hazmat transportation, the PI proposes the use of CVaR on time-dependent networks to determine the safest timing of travel as well as the safest route. In addition, this project will develop an algorithmic framework for solving CVaR-optimal routing problems on time-dependent networks. The algorithm will consists of a line search problem with shortest-path problems on time-dependent networks as subproblems.

The proposed CVaR method is based on two basic data: accident probability and accident consequences. These data are in general subject to large uncertainty, or hard to estimate, because hazmat accidents are rare events and hazmat accident consequences may vary depending on the weather conditions and the characteristics of accidents that are highly stochastic. To address such data uncertainty, a robust optimization method is proposed in combination with CVaR optimization, which provides a mixed integer linear programming problem. The PI will show that the proposed problem can be solved by a numerically tractable algorithm.

Further, the CVaR optimization framework will be extended to consider the total travel time. While the total travel time is a second-hand issue in hazmat transportation due to the importance of safety, in certain cases, consideration of travel time may lead to a much efficient solution with little impact on the safety.

The proposed CVaR optimization may provide a very circuitous path solution, while there may exist some paths which take much shorter time to travel and are almost as safe as the optimal route. In this case, the proposed CVaR models can be combined with total travel time constraints to optimize route choices with reasonable travel time from the origin to the destination. However, the computational complexity quickly increases with the travel time constraint; we need to solve constrained shortest-path problems on time-dependent networks as sub-problems, which are NP-hard. The PI will propose an approximate method based on Lagrangian relaxation. The proposed models and algorithms will be studied in a realistic case of Albany, NY for various scenario tests. The city of Albany, New York is a key junction of major highways and is a hub of hazmat transportation activities. There are altogether seven interstate and US routes that transverse Albany area and its neighborhoods, Rensselaer, Saratoga, and Montgomery: I-90, I-890, I-87, I-787, US-20, US-9 and US-9W. These exhibit a highly variant population density among those areas and dense transportation network along those routes; hence it will provide a good exemplary case study.