基于交叉评价策略的DEA全局协调相对效率排序模型

在DEA(数据包络分析)研究领域,建构在交叉效率概念基础上的现有决策单元排序方法仅以定义的方式给出了用于决策单元排序的交叉效率评价值。对于这种方法构建方式,分别基于管理学的效率概念和多属性决策理论,分析指出其中的交叉效率评价值从本质上讲既与效率的管理学概念不符,也与决策单元的优劣不存在理性逻辑联系。为克服现有决策单元排序方法所存在的上述问题,基于交叉评价策略和效率的管理学概念内涵给出了DEA全局协调相对效率的新概念,在此基础上利用优化理论给出了可以用于决策单元优劣排序的DEA全局协调相对效率测度模型,并通过理论分析和数值案例验证解释了该模型相对于现有决策单元排序方法所拥有的比较优势。     

一种新的基于双前沿面的交叉效率方法及其应用

本文将双前沿面效率评价的思想引入到传统交叉效率模型中，同时，针对双前沿面交叉效率方法中仁慈型和激进型交叉效率策略无法抉择，以及这两种交叉效率策略的应用范围有限的不足，提出了一种新的基于双前沿面的交叉效率方法。该方法的基本思想是选取一个理想决策单元和负理想决策单元，使用被评价决策单元的权重来计算理想决策单元和负理想决策单元的效率，并使被评价决策单元的效率尽可能接近理想解的效率，同时，尽可能远离负理想解的效率。根据该思想，分别在乐观前沿面和悲观前沿面下求解交叉效率值并进行集结，避免了由于前沿面的选择不同导致的差异以及决策者对仁慈型和激进型交叉效率策略进行抉择的困难。最后，将本文方法与现有方法进行对比分析，并将本文方法应用于我国东部地区10个省(直辖市)的创新效率评价中，以验证方法的有效性。     

决策单元交叉效率的自适应群评价方法

传统交叉效率评价方法因决策单元偏好权重不唯一而难以操作,因交叉效率有效性分值平均化集结而难以被接受。目前的学者通常围绕决策单元指标权重的确定性分配方法、交叉效率有效性分值的去平均化集结等分别开展研究。本文将交叉效率评价方法中自评互评相结合的评价模式看作群决策过程,即每个决策单元既是一个被评对象,又是一个决策"专家",提出了一种决策单元交叉效率的自适应群评价方法,将决策单元偏好权重的确定和交叉效率有效性分值的去平均化集结作为同一个决策过程,根据每个决策单元的评价结果与群体评价结果的接近程度,同步迭代调整决策单元的"专家"权重和决策单元自评产生的、并提供给其他被评价决策单元的一组确定的偏好指标权重。实验验证与实例运用分析表明,该方法收敛效果良好,能得到客观稳定的决策单元交叉效率有效性分值及排序。     

基于完全包络面的DEA Super效率评价方法

为了对决策单元进行公平、合理、完全的排序,提出一种考虑完全包络面的DEA Super效率评价方法.讨论包络面的选取与DEA效率值的关系,提出完全包络面的概念,并在等产出图上演示了最优前沿面、最劣前沿面与完全包络面的区别和关系;提出基于最劣前沿面的Super效率DEA模型,给出基于完全包络面的DEA Super效率评价排序模型,目标函数包含决策单元的最优效率和最劣效率两部分.该方法用于决策单元的排序,同时考虑最符合与最不符合决策单元自身偏好的权重体系;该方法用于决策单元的效率排序,能获得比较合理的排序结果,可以实际应用于各种决策单元排序中.     

基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

一种兼顾效率与效果的决策单元投入产出绩效评价方法

在对效率与绩效概念进行甄别的基础上，给出了一种兼顾效率与效果的决策单元投入产出绩效评价方法。有别于决策单元的技术效率评价，该方法一并考虑了决策单元的前沿技术实现与投入产出目的达成。在将决策单元投入产出绩效的影响因素归纳为技术因素、投入配置因素和投入规模因素的基础上，分别构建了决策单元的绩效型综合效率模型、绩效型技术效率模型和绩效型投入配置效率模型。这些模型的解给出了决策单元的投入产出绩效值、决策单元投入产出绩效形成过程中各种影响因素的贡献以及决策单元基于不同影响因素的绩效改进目标，从而为决策单元在现实环境约束下进行绩效提升途径选择提供了较为充分的信息。     

基于理想决策单元参照求解策略的DEA交叉效率评价模型

在已有关于DEA交叉效率评价模型中,激进型模型和仁慈型模型会因评价结果不一致而导致实际应用中难以对它们予以抉择的难题;中立型模型虽在形式上规避了前述问题,但其本身存在着理论偏差。针对上述问题,基于TOPSIS的理想点构造方法,提出了一种关于DEA交叉效率评价的新模型,即基于理想决策单元参照求解策略的DEA交叉效率评价模型。该模型不仅具有理论的严谨性,可以规避激进型模型与仁慈型模型之间的选择难题,而且相对于它们而言能够更好地坚持DEA最有利于被评价决策单元的基本思想。数值模拟分析表明新模型具有解决实际问题的较好适用性。     

基于交叉效率DEA与群体共识的区间乘性语言偏好关系群决策

针对区间乘性语言偏好关系群决策问题，提出了一种基于交叉效率DEA和群体共识的群决策方法。首先，提出乘性语言偏好关系导出函数的定义，并构建产出导向的DEA模型，证明了一致性乘性语言偏好关系的DEA效率得分与排序向量之间存在比例关系。在此基础上，建立基于理想值的交叉效率DEA模型，提出乘性语言偏好关系的通用排序方法。同时，基于群体共识建立目标规划模型来计算各语言偏好关系的权重系数。最后，利用Monte Carlo随机模拟的方法对群体语言偏好空间进行统计分析，得到群决策期望排序向量及其可信度。算例分析表明本文方法能够有效的避免信息损失，具有较强的适用性和较高的可信度。     

中立型两阶段交叉效率评价方法

在数据包络分析中，已有的两阶段交叉效率评价方法，不仅只能用于基本两阶段网络结构，而且没有中立地分解子阶段效率。文章提出了一个既适用于基本两阶段网络结构，又适用于具有共享输入的两阶段网络结构的，中立型交叉效率评价方法。该方法定义自评时整体效率等于子阶段效率的加权和，在自评整体效率最大的前提下，从使各子阶段效率都尽可能大的角度为每个决策单元分别确定一组最优权重，进而通过互评计算决策单元整体和子阶段的最终效率得分。最后，通过两个实例验证了方法的实用、合理、有效。     

存在保证域的模糊超效率DEA模型

模糊DEA模型是用于解决存在模糊数据的决策单元(DMUs)效率评价问题的,然而现有的模糊DEA模型分辨率低,本文构建了存在保证域的模糊超效率DEA模型,并给出了一种基于截集的求解方法并进行了证明,该模型有效地解决了输入和输出全部或部分为模糊数的决策单元全排序问题。最后给出了一个银行效率评价的实例说明了方法的有效性。     

DEA game cross-efficiency approach to Olympic rankings

A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this “chicken and egg” phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.     

The use of OWA operator weights for cross-efficiency aggregation

Cross-efficiency evaluation is an effective way of ranking decision making units (DMUs) in data envelopment analysis (DEA). Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each DMU and view it as the overall performance measurement of the DMU. This paper focuses on the aggregation process of the efficiencies in the cross-efficiency matrix and proposes the use of ordered weighted averaging (OWA) operator weights for cross-efficiency aggregation. The use of OWA operator weights for cross-efficiency aggregation allows the decision maker (DM)’s optimism level towards the best relative efficiencies, characterized by an orness degree, to be taken into consideration in the final overall efficiency assessment and particularly in the selection of the best DMU.     

Exploiting value system multiplicity and preference voting for robust ranking

Under a data envelopment analysis (DEA) framework, full ranking of a group of decision making units (DMUs) can be carried out through an adequate amalgamation of the cross-efficiency (CE henceforth) scores produced for each DMU. In this paper, we propose a ranking procedure that is based on amalgamating the weight profiles selected over the cross-evaluation rather than related CE scores. The new approach builds, for each DMU, a collective weight profile (CWP henceforth) by exploiting the preference voting system embedded within the matrix of weights, which views the assessing DMUs as voters and the input/output factors as candidates. The occurrence of zero votes is discussed as a special case and a two-level aggregation procedure is developed. The CWPs that are produced extend the concept of collective appreciation to the input/output factors of each DMU so that group dynamics is truly reflected, mainly in decision making circumstances where factor prioritization is necessary for making choices or allocating resources. The robustness of the proposed ranking approach is evaluated with three examples drawn from the literature.     

非合作博弈两阶段生产系统DEA并购效率评价

如何选择并购对象及预测并购可行性是企业管理者在并购决策过程中常面临的问题。针对企业并购预测问题,本文以两阶段生产系统的决策单元为研究对象,研究数据包络分析方法在预测并购可行性方面的应用。该生产系统有两个明显的特点:(1)决策单元由两个阶段串行子系统构成,(2)两个子系统一个处于主导地位,而另一个处于从属地位。两个或者两个以上决策单元并购为一个虚拟决策单元。本文在分析由决策单元整体效率与其子系统效率之间关系的基础上,引入非合作博弈的思想,提出了基于非合作博弈的DEA模型评估虚拟决策单元两阶段生产系统的并购效率:即在保持现有的产出水平和生产效率的前提下,分别求解虚拟决策单元及其子系统的并购效率,分析虚拟决策单元如何通过两个子系统实现整个系统的成本节约。最后,将模型应用于台湾24家非寿险保险公司的仿真分析。由于文章提出的方法能够有效地分析虚拟决策单元内部子系统的并购有效性水平,同时考虑子系统之间的主从关系,因此,能够发掘影响虚拟决策单元并购效率的内部因素,因而能够为管理者并购决策提供更精确有效的管理信息,提高并购决策的科学性。     

A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

基于DEA联盟博弈核仁解的固定成本分摊方法研究

本文结合DEA(Data Envelopment Analysis)和联盟博弈理论研究了固定成本分摊问题.本文首先证明了在固定成本作为决策单元(Decision Making Unit,DMU)新投入要素的条件下,那么DMU个体和整体将同为DEA有效,在此结论的基础上,本文结合联盟博弈理论,定义了联盟博弈的特征函数,提出了基于核仁解的固定成本分摊模型,并给出了相应的求解算法,最终通过算例说明了本文方法的合理性和求解算法的可行性.