如何将一定数量的资源在一组决策单元中进行有效地分摊是决策者在实际工作中常面临的问题。本文将决策单元看作系统,研究系统内部为平行结构的资源分摊方法。在将待分摊的资源作为一种新的独立投入要素的前提下,采用数据包络分析(DEA,data envelopment analysis)方法得到能够使得所有的总系统和子平行系统同时达到Pareto有效状态(效率值为1)的资源分摊方案集,并确定每个子平行系统的有效分摊区间。进而定义效用函数以反映各子平行系统对分摊额的满意程度,并基于满意度max-min公平原则和Pareto有效原则建立资源分摊模型。最后通过我国2008年31个省市或地区三大产业的相关数据验证了资源分摊模型的有效性,具有一定的理论与现实指导意义。
Decision makers are often faced with how to allocate a certain amount of resources among peer Decision Making Units (DMUs) effectively in practice. Considering DMUs as systems, this paper focuses on the resource allocation with considering the system structure consisted of a series of parallel subsystems. Treating the allocated resource as a new independent input to DMUs, the allocations ensuring all overall systems and parallel subsystems pareto efficient simultaneously (efficiency values equal to 1) is obtained by employing data envelopment analysis (DEA), and then the efficient interval of allocation for the parallel subsystem is confirmed. The utility function is defined to reflect the satisfaction degree of parallel subsystems to the resource allocation. The final resource allocation model is proposed based on the principles of max-min fairness for satisfaction degrees and Pareto efficient. Finally, the validity of the proposed resource allocation model is demonstrated by the data of the three main industries of 31 provinces or regions in China in 2008. It has theoretical and practical guiding significance in some extent.
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