Humanitarian logistics is an integral part of disaster relief operations, which involves the phases of preparedness, disaster operations, and post-disaster operations. Integrating the planning and execution between phases minimizes the gaps in providing relief to the affected population. This paper presents a two-stage multi-objective mathematical model for integrated decision-making during the preparation and response phases. The proposed model is developed to jointly optimize the location of emergency shelters (and/or depots) and coordinate the movement of relief vehicles between the disaster site and emergency shelters. Focusing on the optimal distribution of relief supplies to the emergency shelters, the proposed model aims to minimize the operational, distributive injustice, and dissatisfaction costs. To address the computational complexity of the introduced model, two multi-objective meta-heuristics, namely multi-objective vibration damping optimization and non-dominated sorting genetic algorithm (NSGA-II), are used. A comprehensive sensitivity analysis is conducted to study the impacts of variations in key parameters on model output under different scenarios. Our results suggests that the employed solution algorithms outperform the traditional optimization methods in achieving the Pareto-Front solutions.

人道主义后勤是救灾行动不可或缺的一部分，它涉及准备，灾难行动和灾后行动的各个阶段。在各个阶段之间整合计划和执行，可以最大程度地减少为受影响人口提供救济的差距。本文提出了一个两阶段的多目标数学模型，用于在准备和响应阶段进行综合决策。提出的模型旨在共同优化应急避难所（和/或仓库）的位置，并协调救灾车辆在灾区和应急避难所之间的移动。该模型着重于向紧急避难所提供救济物资的最佳分配，旨在最大程度地减少运营，分配上的不公正和不满成本。为了解决引入模型的计算复杂性，使用了两个多目标元启发式算法，即多目标振动阻尼优化和非支配排序遗传算法（NSGA-II）。进行了全面的敏感性分析，以研究关键参数变化对不同情况下模型输出的影响。我们的结果表明，在实现Pareto-Front解决方案时，所采用的解决方案算法优于传统的优化方法。