A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

DEA有效单元排序的一种新方法

通过对DEA有效单元排序中超有效性方法的探讨,提出了一种新的方法.利用对构造模型目标函数的处理,新的方法能够实现对有效单元的完全排序.最后,通过两个算例进一步验证了新方法的可行性和优越性.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

用超效率综合DEA模型来研究DEA有效性

对超效率综合DEA模型,有三个定理来判断其不可行性,其中一个定理基于加性模型来判断,并证明:当模型不可行时被评决策单元的扩展DEA有效性,由此给出了对扩展DEA有效的决策单元排序的方法,此外,对不含非阿基米德无穷小的基于输入(输出)的超效率综合DEA模型,当其最优值为1时,有一个定理来判断被评单元的DEA有效性.     

A Euclidean distance-based measure of efficiency in data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). Several efficiency measures have been proposed in the DEA literature, see, for instances, radial efficiency measure of Charnes et al. (CCR)(A. Charnes. W.W. Cooper, and E. Rhodes, 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–444), Russell graph measure (J.T. Russell, and R. Sirvant. 1999. An enhanced DEA Russell graph efficiency measure. Eur. J. Oper. Res. 115, pp. 596–607) and slack-based measure of Tone (K. Tone, 2001. A slack-based measure of efficiency in DEA. Eur. J. Oper. Res. 130, p. 498–509). In this article, we will propose an Euclidean distance-based measure of efficiency. Then, in order to discriminate the performance of efficient DMUs, an alternative super-efficiency DEA model is proposed. The applicability of the models developed is illustrated in the context of the analysis of gas companies performance.     

A new method for complete ranking of DMUs

So far numerous models have been proposed for ranking the efficient decision-making units (DMUs) in data envelopment analysis (DEA). But, the most shortcoming of these models is their two-stage orientation. That is, firstly we have to find efficient DMUs and then rank them. Another flaw of some of these models, like AP-model (A procedure for ranking efficient units in data envelopment analysis, Management Science, 39 (10) (1993) 1261–1264), is existence of a non-Archimedean number in their objective function. Besides, when there is more than one weak efficient unit (or non-extreme efficient unit) these models could not rank DMUs. In this paper, we employ hyperplanes of the production possibility set (PPS) and propose a new method for complete ranking of DMUs in DEA. The proposed approach is a one stage method which ranks all DMUs (efficient and inefficient). In addition to ranking, the proposed method determines the type of efficiency for each DMU, simultaneously. Numerical examples are given to show applicability of the proposed method.     

薄膜型声学超材料对低频振动的隔声特性分析*

高效共振混合机工作频率为60 Hz,且系统处于共振,产生较大低频噪声。针对振动机械产生的有害噪声,分析了高效共振混合机低频高加速度共振混合过程的特点,得到了60 Hz低频声波穿透力强特点,相比传统的以吸声材料构建的50~100 mm厚度、隔声效果小于10 dB的隔声罩,分析了薄膜型声学超材料在低频减振降噪中的隔声特性。通过多物理场仿真分析,60 Hz时隔声量为31.4 dB,确定了硅橡胶弹性薄膜的预应力和质量块的面密度;采用3D打印机快速成型技术,构建了隔声实验装置,分析了独立隔声单元、面密度、薄膜尺寸等隔声特性规律。基于人耳在实际环境中感受到的噪声强度,提出了噪声衰减量和插入损失的分析方法,在距离声源380 mm和1000 mm的位置,60 Hz时隔声量分别为27 dB和38 dB。研究成果丰富了低频隔声特性理论,为薄膜型声学超材料的工程设计和优化提供了技术支撑。     

广义超效率区间DEA模型及其有效性研究

根据样本单元的区间投入、区间产出定义最大样本生产可能集,建立基于最大样本生产可能集的广义超效率区间DEA模型,然后定义了待评价决策单元基于广义超效率区间DEA模型的超效率区间,并讨论了待评价决策单元的有效性,最后通过实例表明了广义超效率区间DEA模型的实用性.     

县域三次产业虚拟标杆的建立及应用研究——以海南省县域为例

为了解决县域三次产业标杆不属于同一组织(市县)的问题,基于县域三次产业投入产出数据,使用超效DEA-Malmquist和面板数据模型,建立了将县域三次产业优势和谐地统一到一体的虚拟标杆.应用虚拟标杆理论实证分析了海南省县域三次产业,并以万宁市作为虚拟标杆的实施者,给出了万宁市三次产业资源配置的优化决策.结果表明,构建县域三次产业虚拟标杆对提高标杆实施者的三次产业效率具有显著的作用.     

考虑非期望因素的决策单元排序:两阶段综合效率法

对所有平行级别上的同等类型的决策单元(DMUs)在绩效表现上的排序一直是管理决策领域研究的重要课题之一。基于数据包络分析的超效率理论和SBM模型,探讨考虑非期望因素的DMUs排序问题。首先构建新的考虑非期望因素的超效率SBM模型,此模型不仅能对有效DMUs排序,而且能够转化成线性规划问题求解,具有有界性、单调性等良好性质。然后将新模型与Tone的SBM模型结合提出了考虑非期望因素的SBM综合排序法,同时给出了相对应的多项式时间算法。该方法以SBM模型作为第一阶段完成非有效DMUs排序,以新模型作为第二阶段完成有效DMUs排序,两阶段综合即完成所有DMUs排序。研究结果表明,综合排序法能够完成对考虑非期望因素的DMUs的排序,为绩效评价的管理实践提供了重要的理论依据。选取中国2010年的30个省份为实证研究对象,应用所提出的综合效率排序法对其环境效率进行排序。分析结果与中国的现实情况的相吻合,表明该排序方法是合理的,能够完成对这些地区的环境效率进行排序,可以为决策者评价环境的绩效表现提供有效的决策支持。