## Introduction Humanitarian aid distribution is a critical aspect of post-disaster logistics. However, the limited resources available can make it challenging to meet all the needs of affected communities. In this context, our team of experts has developed a new optimization algorithm to overcome these limitations. ## Problem Formulation The problem at hand is that of planning vehicle routes from a distribution center to shelters while allocating limited relief supplies in an equitable manner. Our goal is to reduce inequality in unsatisfied demand for fair distribution and minimize total travel time for timely delivery. ## Proposed Solution To address this bi-objective problem, we have proposed a mixed integer programming (MIP) model and used the ฮต-constraint method to handle its bivariate nature. We have also derived mathematical properties of the optimal solution and introduced valid inequalities to design an algorithm for optimal delivery allocations given feasible vehicle routes. ## Branch-and-Price Algorithm Our new algorithm, called "branch-and-price," is designed to efficiently solve the problem. The branch-and-price technique combines linear optimization with applied techniques for non-linear problems. ## Testing and Results We have conducted computational tests on realistic datasets from a past earthquake in Van, Turkey, and predicted data for Istanbul's Kartal region. The results show that our algorithm significantly outperforms commercial MIP solvers in terms of time resolution and quality of solutions. ## Conclusion Our "branch-and-price" algorithm represents a significant step forward in logistics planning for effective and rapid humanitarian aid. The 34% reduction in inequity without compromising efficiency demonstrates the importance of considering both objectives during supply planning.