Mathematical Models for Evacuation Planning in Urban Areas (Lecture Notes in Economics and Mathematical Systems Book 659)

Introduction -- Literature Review -- An Urban Evacuation Problem -- A Relaxation-Based Heuristic Approach for the Mixed-Integer Evacuation Model -- A Pattern-Based Evacuation Planning Model for Urban Areas -- A Two-Staged Heuristic Approach -- A Multicommodity Urban Evacuation Problem -- A Four-Staged Heuristic Approach to Solve the Urban Multicommodity Model -- Conclusions and Future Research -- Erratum to: Mathematical Models for Evacuation Planning in Urban Areas Cover......Page 1 Mathematical Models for Evacuation Planning in Urban Areas......Page 4 Preface......Page 6 Contents......Page 8 List of Figures......Page 12 List of Tables......Page 16 1.1 Evacuation Planning......Page 18 1.2 Basic Network Flow Problems......Page 21 1.2.1 A Generic Network Flow Model......Page 24 1.2.2 A Generic Network Flow Model with Waiting on Arcs......Page 25 1.2.3 Objectives......Page 27 1.3 Crossing and Merging Conflicts......Page 29 1.4 Chapter Synopsis......Page 31 References......Page 32 2.1 Flow-Based Optimization Models......Page 34 2.2 Evacuation Models with Traffic Management Strategies......Page 43 2.3 Further Problems in Evacuation Planning......Page 45 2.4 Simulation Approaches......Page 47 2.5 Summary......Page 49 References......Page 50 3 An Urban Evacuation Problem......Page 56 3.1 A Network Representation......Page 57 3.2.1 Decision Variables and Additional Parameters......Page 60 3.2.2 Model Formulation......Page 62 3.3 An Extension of the Urban Evacuation Model: Waiting on Arcs......Page 70 3.4 An Extension of the Urban Evacuation Model: A One-Way Evacuation Model......Page 73 3.5 Examples of the Variations of the Urban Evacuation Model......Page 76 3.5.1 An Example Considering Different Objective Functions......Page 77 3.5.2 An Example Considering Evacuation Models with and without Waiting......Page 79 3.5.3 An Example Considering the Two-Way and One-Way Model......Page 82 References......Page 83 4.1 A Relaxation-Based Heuristic Solution Approach......Page 84 4.1.1 Preliminary Considerations......Page 86 4.1.2 Adjustment Algorithm......Page 94 4.3 Computational Study......Page 104 4.3.1 Computational Study: Two-Way Heuristic Approach......Page 107 4.3.2 Computational Study: One-Way Heuristic Approach......Page 113 References......Page 117 5.1 A One-Stage Pattern-Based Urban Evacuation Model......Page 118 5.2 Patterns of Street Sections Between Intersections......Page 124 5.3 Patterns of Intersections......Page 125 5.3.1 Graphs and Patterns of Intersections......Page 126 5.3.2 Number of Crossing Conflicts......Page 129 5.3.3 Planar Graphs and Patterns......Page 133 References......Page 145 6.1 First Stage of the Heuristic......Page 146 6.2 Second Stage of the Heuristic......Page 150 6.3 Computational Study......Page 153 6.3.1 Sets of Instances......Page 154 6.3.2 Models for Comparison......Page 155 6.3.3 Computational Results......Page 156 Reference......Page 161 7.1 Introduction and Assumptions......Page 162 7.2.1 A Network Representation......Page 166 7.2.2 Parameters and Variables......Page 167 7.2.3 Objective and Constraints......Page 169 7.3 An Illustration of Solutions of the Multicommodity Urban Evacuation Model......Page 174 8 A Four-Staged Heuristic Approach to Solve the Urban Multicommodity Model......Page 179 8.1 First Stage of the Multicommodity Heuristic......Page 181 8.2 Second Stage of the Multicommodity Heuristic......Page 185 8.3 Third Stage of the Multicommodity Heuristic......Page 189 8.4 Fourth Stage of the Multicommodity Heuristic......Page 196 8.5 Computational Study......Page 197 9 Conclusions and Future Research......Page 201 References......Page 205 Erratum to: Mathematical Models for Evacuation Planning in Urban Areas......Page 109 Erratum to: Mathematical Models for Evacuation Planning in Urban Areas......Page 207 A.2 Network Representation......Page 208 Disasters like floods, hurricanes, chemical or nuclear accidents may cause the necessity to evacuate the affected area. The evacuation of the urban area needs to be planned carefully. One issue is the reorganization of the traffic routing. Congested urban areas have usually complex street networks that are composed of many intersections with streets connecting them. The population density of a congested urban area is usually high and the street network is already used to capacity during rush hour traffic. The considered problem of this work is the reorganization of the traffic routing of an urban area for the case of an emergency mass evacuation. Especially aspects of the evacuation like safety, avoidance of delays and the total system travel time are taken into account. Combinatorial and graph theoretical aspects are adapted for the evacuation problem and highlight issues concerning especially conflicts within intersections. This work gives an extensive summary of literature of evacuation of urban areas. Mixed-integer linear programming models are developed for evacuation problems and heuristic algorithms are provided and tested.?