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

TL;DR

This paper introduces a branch-and-price algorithm for efficient and fair last-mile relief aid distribution, balancing equity and timeliness in post-disaster logistics through a bi-objective optimization model.

Contribution

It develops a novel B&P algorithm for solving a bi-objective relief distribution problem, incorporating mathematical properties and valid inequalities for improved efficiency.

Findings

B&P algorithm outperforms commercial solvers on realistic datasets.

Bi-objective approach reduces inequity by 34% without losing efficiency.

Prioritizing demand coverage over fairness is effective under tight time constraints.

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 $\epsilon$-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.