A Branch-and-Price Algorithm for Fast and Equitable Last-Mile Relief Aid Distribution

• URL: http://arxiv.org/abs/2512.19882v1
• Date: Mon, 22 Dec 2025 21:16:52 GMT
• Title: A Branch-and-Price Algorithm for Fast and Equitable Last-Mile Relief Aid Distribution
• Authors: Mahdi Mostajabdaveh, F. Sibel Salman, Walter J. Gutjahr,
• Abstract summary: In disasters, prepositioned supplies often fall short of meeting all demands.<n>We address the problem of planning vehicle routes from a distribution center to shelters while allocating limited relief supplies.<n>Our bi-objective approach reduces aid distribution inequity by 34% without compromising efficiency.
• Score: 0.910208503367801
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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