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\rEvacuation Planning in Urban Areas......Page 207
A.2 Network Representation......Page 208