Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming

Hamoud Bin Obaid, Theodore B. Trafalis, Mastoor M. Abushaega (), Abdulhadi Altherwi and Ahmed Hamzi
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Hamoud Bin Obaid: Department of Industrial Engineering, King Saud University, Riyadh 11421, Saudi Arabia
Theodore B. Trafalis: Department of Industrial and Systems Engineering, University of Oklahoma, 202 W Boyd St. Lab 28, Norman, OK 73019, USA
Mastoor M. Abushaega: Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia
Abdulhadi Altherwi: Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia
Ahmed Hamzi: Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2024, vol. 13, issue 1, 1-25

Abstract: This study presents a new approach to optimize the dynamic evacuation process through a dynamic traffic assignment model formulated using mixed-integer linear programming (MILP). The model approximates the travel time for evacuee groups with a piecewise linear function that accounts for variations in travel time due to load-dependent factors. Significant delays are transferred to subsequent groups to simulate delay propagation. The primary objective is to minimize the network clearance time—the total time required for the last group of evacuees to reach safety from the start of the evacuation. Given the model’s computational intensity, a simplified version is introduced for comparison. Both the original and simplified models are tested on small networks and benchmarked against the Cell Transmission Model, a well-regarded method in dynamic traffic assignment literature. Additional objectives, including average travel time and average evacuation time, are explored. A sensitivity analysis is conducted to assess how varying the number of evacuee groups impacts model outcomes.

Keywords: evacuation planning; disaster management; optimal routing; mixed-integer linear programming; dynamic traffic assignment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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