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

arXiv: https://arxiv.org/abs/2512.19882 · HTML: https://mlsanity.com/paper/2512.19882/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 75 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 3 of 3)

- [A concise guide to existing and emerging vehicle routing problem variants](https://mlsanity.com/paper/1906.06750/) (2019)
- [Workload Equity in Vehicle Routing Problems: A Survey and Analysis](https://mlsanity.com/paper/1605.08565/) (2016)
- [Revisiting Gini for equitable humanitarian logistics](https://mlsanity.com/paper/2106.12686/) (2021)

## Abstract (arXiv)

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.