Modeling demand management strategies for evacuationsby Hediye Tuydes-Yaman, Athanasios Ziliaskopoulos

Annals of Operations Research

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Year
2014
DOI
10.1007/s10479-014-1533-6
Subject
Decision Sciences (all) / Management Science and Operations Research

Text

Modeling demand management strategies for evacuations

Hediye Tuydes-Yaman • Athanasios Ziliaskopoulos

Published online: 4 March 2014  Springer Science+Business Media New York 2014

Abstract Evacuations are massive operations that create heavy travel demand on road networks some of which are experiencing major congestions even with regular traffic demand. Congestion in traffic networks during evacuations, can be eased either by supply or demand management actions. This study focuses on modeling demand management strategies of optimal departure time, optimal destination choice and optimal zone evacuation scheduling (also known as staggered evacuation) under a given fixed evacuation time assumption. The analytical models are developed for a system optimal dynamic traffic assignment problem, so that their characteristics can be studied to produce insights to be used for large-scale solution algorithms. While the first two strategies were represented in a linear programming (LP) model, evacuation zone scheduling problem inevitable included integers and resulted in a mixed integer LP (MILP) one. The dual of the LP produced an optimal assignment principle, and the nature of the MILP formulations revealed clues about more efficient heuristics. The discussed properties of the models are also supported via numerical results from a hypothetical network example.

Keywords Demand management models for evacuations  Linear programming models  System optimum dynamic traffic assignment  Departure time optimization  Destination optimization  Evacuation zone scheduling 1 Introduction

Traffic management during evacuations of urban locations is a challenging task, especially if the network is already congested even for the typical everyday demand. The disaster

H. Tuydes-Yaman (&)

Civil Engineering Department, Middle East Technical University, Ankara, Turkey e-mail: htuydes@metu.edu.tr

A. Ziliaskopoulos

University of Thesseloniki, Vo´los, Greece e-mail: ziliasko@mie.uth.gr 123

Ann Oper Res (2014) 217:491–512

DOI 10.1007/s10479-014-1533-6 conditions can only worsen when origin–destination (O–D) demand patterns change drastically and people are massively trying to evacuate the urban area; conditions can be further exacerbated by possible loss of capacity during or after the disaster. Since it is not financially feasible to design the transportation network for rare evacuation occurrences, it is possible to speed up the evacuation by employing either some supply management options, such as contraflow corridors, etc., studied at different levels in the literature (Tuydes 2005; Tuydes and Ziliaskopoulo 2006; Wolshon and Lambert 2006), or by some demand management actions, which will be discussed in this study.

Though less commonly used, it is important to see the potential improvements that can be achieved by demand management policies for evacuations. Because, if there are any delays in the deployment of the evacuation due to management, weather factors, legal issues, etc., the evacuation time window calculated based on regular capacity or supply management tools may be passed, and more drastic measures, such as demand management strategies may be needed. The shorter the safe evacuation time window is, the more critical and effective the demand management strategies can be.

In this paper, first a brief discussion of literature of evacuation models is presented with a special focus on those with demand management issues. To provide a background for the proposed models, major issues of evacuation models are discussed, which is followed by a base mathematical model that optimizes route and destination choices, and departure times for Fixed Evacuation Time (FET) assumption in the first part of Sect. 3. Later, a mathematical model that produces optimal evacuation zone scheduling plan with assumed demand mobilization durations at the origins is presented. Properties of these models are discussed briefly in Sect. 4, which are important to develop algorithms for large-scale networks; but the numerical part of the study provides only analytical solutions for different demand management strategy in Sect. 5. Heuristic algorithms and large-scale applications of the models can be found in Tuydes (2005). 2 Background

Literature on disaster studies as well as Traffic Assignment modeling (static and dynamic) is extensively reviewed by Tuydes (2005). Here, highlights of the evacuation modeling over the decades and recent developments in the demand management issues will be summarized first. In the last part, general properties of Traffic Assignment models for evacuations will be discussed providing the necessary background to understand the proposed Demand Management Models that will be introduced later. 2.1 Evacuation model studies

A major leap of evacuation models was created in 1980s after a mandate by Nuclear

Regulatory Commission for preparation of evacuation plans around nuclear power plants (Voorhees 1982; Cosby and Powers 1982; KLD Associates, Inc. 1982). A study of evacuation management alternatives (including rearrangement of gathering points, traffic signal improvement and using partial reversibility lanes on 6-lane highways) via a macroscopic model by Han (1990) showed that integrated solutions added a bigger impact by decreasing evacuation time, as opposed to sum of individual effects gained by partial improvements alone.

A second wave of advances in evacuation models came with the state-wide preparedness efforts supported by the Federal Emergency Management Agency (FEMA) for the 492 Ann Oper Res (2014) 217:491–512 123 hurricane prone regions in the southeastern USA in 1990s. The studies in the early 1990s are mostly concerned with the evaluation of emergency actions undertaken during Hurricane Hugo, and considered additional parameters of trip generation, as well as human response to evacuation order, definition and priorities of evacuation regions, and reversibility of the critical parts of the network capacity (Lewis 1990; Sexton 1990). Other studies that appeared in the literature discussed planning approaches for hurricane evacuations from the police perspective, focusing on the implementation of policies as well as safety issues, giving practical insights into the program, such as coordination of fire and emergency teams of the local and neighboring towns and cities, people deciding not to leave because their pets are not allowed at the shelters, etc. to develop more realistic models for the following studies (Patterson and Shelor 1993; Thurber 1995; Getz 1996;