Abstract: On account of resources allocation problems, a decision method based on classification is proposed to achieve the trade-off between efficiency and equity goals. Firstly, the efficiency optimal and completely equal allocation methods are studied to reveal the influence of marginal utilities on allocation results. It shows that the smaller the difference between the marginal utilities is, the closer the allocation results of those two methods. Then the 0-1 integer programming model is established to solve the clustering results with the objection of minimizing the gaps between class marginal utilities. And the resources are allocated by the efficiency optimal method among classes, while completely equal allocation method within each class. The amount of classes can result in different degrees of equity. Finally, a numerical example proves the validity and indicates how the amount of classes affects the efficiency and equity.

Key words: resources allocation, equity, classification, 0-1 integer programming model

摘要： 针对资源分配问题,本文提出了基于分类的决策方法以实现效率与公平的权衡。首先,研究了效率最优分配与完全均等分配过程,阐明了边际效用对分配结果的影响,指出个体间边际效用相差越小,两种分配的结果越接近。其次,构建0-1整数规划模型求解分类结果,目标是使类与类之间边际效用相差尽可能小。然后,按类对资源进行分配,类间采用完全均等分配,类中采用效率最优分配。通过选择分类数量可以实现不同程度的公平。最后,运用算例验证方法的有效性,说明分类数量对效率与公平的影响。

关键词: 资源分配, 公平, 分类, 0-1整数规划