Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming
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 i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/12 |
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| author | Hamoud Bin Obaid Theodore B. Trafalis Mastoor M. Abushaega Abdulhadi Altherwi Ahmed Hamzi |
| author_facet | Hamoud Bin Obaid Theodore B. Trafalis Mastoor M. Abushaega Abdulhadi Altherwi Ahmed Hamzi |
| author_sort | Hamoud Bin Obaid |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2a40e7b28d704c69bb229f3b9fbaffa4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2a40e7b28d704c69bb229f3b9fbaffa42025-01-10T13:17:57ZengMDPI AGMathematics2227-73902024-12-011311210.3390/math13010012Optimizing Dynamic Evacuation Using Mixed-Integer Linear ProgrammingHamoud Bin Obaid0Theodore B. Trafalis1Mastoor M. Abushaega2Abdulhadi Altherwi3Ahmed Hamzi4Department of Industrial Engineering, King Saud University, Riyadh 11421, Saudi ArabiaDepartment of Industrial and Systems Engineering, University of Oklahoma, 202 W Boyd St. Lab 28, Norman, OK 73019, USADepartment of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi ArabiaThis 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.https://www.mdpi.com/2227-7390/13/1/12evacuation planningdisaster managementoptimal routingmixed-integer linear programmingdynamic traffic assignment |
| spellingShingle | Hamoud Bin Obaid Theodore B. Trafalis Mastoor M. Abushaega Abdulhadi Altherwi Ahmed Hamzi Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming Mathematics evacuation planning disaster management optimal routing mixed-integer linear programming dynamic traffic assignment |
| title | Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming |
| title_full | Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming |
| title_fullStr | Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming |
| title_full_unstemmed | Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming |
| title_short | Optimizing Dynamic Evacuation Using Mixed-Integer Linear Programming |
| title_sort | optimizing dynamic evacuation using mixed integer linear programming |
| topic | evacuation planning disaster management optimal routing mixed-integer linear programming dynamic traffic assignment |
| url | https://www.mdpi.com/2227-7390/13/1/12 |
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