重新审视基尼问题，以促进公平的人道主义后勤工作
Revisiting Gini for equitable humanitarian logistics
摘要：
在人道主义物流领域，稀缺资源的公平分配模型是一个快速增长的问题。基尼系数是公认的衡量不平等的最广泛的标准之一，它最初是通过洛伦兹曲线来表征的，洛伦兹曲线是一个数学函数，将收入的累积份额与人口中的等级序群联系起来。到目前为止，使用基尼系数来处理公平问题的人道主义后勤模式实际上并没有优化其最初的提法，而是使用了不一定重复最初基尼系数的其他定义。本文通过洛伦兹曲线推导出原始基尼系数，以优化人道主义选址分配问题中的效率与公平权衡。我们还提出了新的有效的不等式的基础上的上界洛伦兹曲线收紧我们的模型的线性松弛，并开发一个基于聚类的洛伦兹曲线，需要更少的额外的约束和变量比原来的构造。基于巴西里约热内卢州洪水和山体滑坡的计算研究表明，虽然替代基尼系数定义具有有趣的特性，但与原始基尼系数相比，它们可以产生截然不同的决策。此外，从原始基尼系数的角度来看，这些决定可能会大大降低公平性。
英文摘要：
Modeling equity in the allocation of scarce resources is a fast-growing concern in the humanitarian logistics field. The Gini coefficient is one of the most widely recognized measures of inequity and it was originally characterized by means of the Lorenz curve, which is a mathematical function that links the cumulative share of income to rank-ordered groups in a population. So far, humanitarian logistics models that have approached equity using the Gini coefficient do not actually optimize its original formulation, but use alternative definitions that do not necessarily replicate that original Gini measure. In this paper, we derive the original Gini coefficient via the Lorenz curve to optimize the effectiveness-equity trade-off in a humanitarian location-allocation problem. We also propose new valid inequalities based on an upper-bounding Lorenz curve to tighten the linear relaxation of our model and develop a clustering-based construction of the Lorenz curve that requires fewer additional constraints and variables than the original one. The computational study, based on the floods and landslides in Rio de Janeiro state, Brazil, reveals that while alternative Gini definitions have interesting properties, they can generate vastly different decisions compared to the original Gini coefficient. In addition, viewed from the perspective of the original Gini coefficient, these decisions can be significantly less equitable.
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