A branch-and-price algorithm for fast and equitable last-mile relief aid distribution

Mahdi Mostajabdaveh, F. Sibel Salman and Walter J. Gutjahr

European Journal of Operational Research, 2025, vol. 324, issue 2, 522-537

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.

Keywords: Humanitarian logistics; Equitable aid distribution; Multi-objective; Branch-and-Price (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:324:y:2025:i:2:p:522-537

DOI: 10.1016/j.ejor.2025.01.032

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