Balancing the trade-off between efficiency and equity in a stochastic emergency supplies allocation problem - Huang, Shihong; Zhu, Hongyi; Wang, Hongyuan; Liu, Kanglin; Liu, Xiaohang; Zhang, Zhi-Hai (Applied mathematical modelling, 2025)
Emergency supplies, including essentials such as food, water, tents, and medicines, often face shortages immediately following a disaster. Uneven distribution of these supplies can result in disparities in assistance, making equity a crucial objective in humanitarian logistics. Given the typically limited relief budgets, we add another objective that minimizes the total operational cost, which is composed of inventory and transportation costs. To achieve both goals simultaneously, this paper proposes a bi-objective programming model that aims to increase relief efficiency by minimizing the total operational cost while also capturing distribution equity through a quantitative index inspired by the Gini index. We develop a stochastic programming framework to account for demand uncertainty. The proposed nonlinear bi-objective two-stage stochastic programming model is transformed into a mixed-integer linear program via the ϵ-constraint method and a scenario-based approach. To address computational challenges, we implement a branch-and-cut-based L-shaped algorithm with several acceleration techniques. On the basis of an empirical case study focusing on the mask distribution process in Pudong New Area, Shanghai, our findings indicate the following: (i) the accelerated algorithm improves the computational efficiency; (ii) the proposed two-stage stochastic scheme outperforms its deterministic counterpart, and (iii) the proposed equity-promoting bi-objective model leads to a more diverse distribution. •Bi-objective model balances cost-efficiency and equity in humanitarian logistics.•Gini-index-inspired metric ensures equitable relief distribution.•Stochastic programming addresses demand uncertainty in operations.•Branch-and-cut L-shape algorithm boosts computational efficiency.•Shanghai case study demonstrates improved distribution diversity and efficacy.