A Branch-and-Price Algorithm for Fast and Equitable Last-Mile Relief Aid Distribution
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909974416850944 |
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| author | Mostajabdaveh, Mahdi Salman, F. Sibel Gutjahr, Walter J. |
| author_facet | Mostajabdaveh, Mahdi Salman, F. Sibel Gutjahr, Walter J. |
| contents | The distribution of relief supplies to shelters is a critical aspect of post-disaster humanitarian logistics. In major disasters, prepositioned supplies often fall short of meeting all demands. We address the problem of planning vehicle routes from a distribution center to shelters while allocating limited relief supplies. To balance efficiency and equity, we formulate a bi-objective problem: minimizing a Gini-index-based measure of inequity in unsatisfied demand for fair distribution and minimizing total travel time for timely delivery. We propose a Mixed Integer Programming (MIP) model and use the $ε$-constraint method to handle the bi-objective nature. By deriving mathematical properties of the optimal solution, we introduce valid inequalities and design an algorithm for optimal delivery allocations given feasible vehicle routes. A branch-and-price (B&P) algorithm is developed to solve the problem efficiently. Computational tests on realistic datasets from a past earthquake in Van, Turkey, and predicted data for Istanbul's Kartal region show that the B&P algorithm significantly outperforms commercial MIP solvers. Our bi-objective approach reduces aid distribution inequity by 34% without compromising efficiency. Results indicate that when time constraints are very loose or tight, lexicographic optimization prioritizing demand coverage over fairness is effective. For moderately restrictive time constraints, a balanced approach is essential to avoid inequitable outcomes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Branch-and-Price Algorithm for Fast and Equitable Last-Mile Relief Aid Distribution Mostajabdaveh, Mahdi Salman, F. Sibel Gutjahr, Walter J. Artificial Intelligence Optimization and Control The distribution of relief supplies to shelters is a critical aspect of post-disaster humanitarian logistics. In major disasters, prepositioned supplies often fall short of meeting all demands. We address the problem of planning vehicle routes from a distribution center to shelters while allocating limited relief supplies. To balance efficiency and equity, we formulate a bi-objective problem: minimizing a Gini-index-based measure of inequity in unsatisfied demand for fair distribution and minimizing total travel time for timely delivery. We propose a Mixed Integer Programming (MIP) model and use the $ε$-constraint method to handle the bi-objective nature. By deriving mathematical properties of the optimal solution, we introduce valid inequalities and design an algorithm for optimal delivery allocations given feasible vehicle routes. A branch-and-price (B&P) algorithm is developed to solve the problem efficiently. Computational tests on realistic datasets from a past earthquake in Van, Turkey, and predicted data for Istanbul's Kartal region show that the B&P algorithm significantly outperforms commercial MIP solvers. Our bi-objective approach reduces aid distribution inequity by 34% without compromising efficiency. Results indicate that when time constraints are very loose or tight, lexicographic optimization prioritizing demand coverage over fairness is effective. For moderately restrictive time constraints, a balanced approach is essential to avoid inequitable outcomes. |
| title | A Branch-and-Price Algorithm for Fast and Equitable Last-Mile Relief Aid Distribution |
| topic | Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2512.19882 |