Reliability analysis of evacuation routes under capacity uncertainty of road links

Abstract

This article presents a reliability-based evacuation route planning model that seeks to find the relationship between the clearance time, number of evacuation paths, and congestion probability during an evacuation. Most of the existing models for network evacuation assume deterministic capacity estimates for road links without taking into account the uncertainty in capacities induced by myriad external conditions. Only a handful of models exist in the literature that account for capacity uncertainty of road links. A dynamic network–based evacuation model is extended by incorporating probabilistic arc capacity constraints and a minimum-cost network flow problem is formulated that finds a lower bound on the clearance time within the framework of a chance-constrained programming technique. Network breakdown minimization principles for traffic flow in evacuation planning problem are applied and a path-based evacuation routing and scheduling model is formulated. Given the horizon time for evacuation, the model selects the evacuation paths and finds flows on the selected paths that result in the minimum congestion in the network along with the reliability of the evacuation plan. Numerical examples are presented and the effectiveness of the stochastic models in evacuation planning is discussed. It is shown that the reliability-based evacuation plan is conservative compared with plans made using a deterministic model. Stochastic models guarantee that congestion can be avoided with a higher confidence level at the cost of an increased clearance time.

Keywords:

• Dynamic network flow problem
• stochastic capacity
• emergency evacuation
• reliability
• chance-constrained programming

Additional information

Notes on contributors

Gino J. Lim

Gino Lim is the Chair of Industrial Engineering and Hari and Anjali faculty fellow at the University of Houston. He is the founding director of Systems Optimization and Computing Laboratory (SOCL) at the University of Houston. His research interests are in mathematical modeling and designing computationally efficient algorithms for large-scale optimization models. His primary application areas include medical decision making, health systems, and homeland security. He was the recipient of the Pierskalla Best Paper award (INFORMS) for his pioneering work on gamma knife radiotherapy optimization for brain cancer patients. His research projects are well funded by federal, state, and local agencies and include maritime security, global supply chain under disruption, emergency evacuation planning and management, radiation treatment planning, hospital staff scheduling, and high-performance computing. His papers have been published in journals such as Informs Journal on Computing, IIE Transactions, SIAM Journal on Optimization, European Journal of Operational Research, and Annals of Operations Research. He has received numerous teaching excellence awards and outstanding service awards. He received both his M.S. and Ph.D. degrees in Industrial Engineering from the University of Wisconsin–Madison.

Mukesh Rungta

Mukesh Rungta received his M.S. degree in Electrical Engineering and Ph.D. in Industrial Engineering from the University of Houston. He is currently a Research Scientist at Air Liquide, where his focus is on optimizing the strategic supply chain. He is also working on robust production scheduling optimization and energy risk management.

M. Reza Baharnemati

Mohammad Reza Baharnemati is a Senior Systems Engineer at Innovative Scheduling, LLC. He received his Ph.D. in Industrial Engineering from the University of Houston. His research interests are in mathematical modeling and designing computationally efficient algorithms for large-scale optimization models. His primary application areas include transportation, logistics, and big data analytics. He has been the recipient of several awards, including student best paper, best teaching assistant, and chairman leadership award while he was doing is Ph.D. His papers have been published in Transportation Science, IIE Transactions, European Journal of Operational Research, and Annals of Operations Research, to name a few. He is currently managing a project in the area of big data analytics that aims to build a tool that collects large amounts of data of various types and stores and analyzes to uncover hidden patterns and unknown correlations.