利润最大问题与弱DEA有效(C2GS2)

对利润最大问题[1]本文用不同于文[1]的方法来讨论.通过解这一个问题,不但知道在一定条件下有最大利润的决策单元的弱DEA有效性(C2GS2),而且找到所有有最大利润的决策单元.     

加性DEA模型与规模收益

[1]给出了用C^2R模型或C^2GS^2模型来判断决策单元的规模收益情况的定理,指出它有时失效。对DEA有效（C^2GS^2）的决策单元,本用加性DEA模型来有效地判断其规模收益情况。     

具有摄动的两类马氏决策规则

在状态空间和行动集均有限的条件下,[1-5]讨论了时间离散的,平稳的马氏决策规划的摄动模型,其中,[1,3,4]讨论了单摄动模型,[5]讨论了具有加权准则的摄动模型,[6,7]讨论了时间离散的,平稳的马氏报酬过程的摄动模型,但[6,7]仅考虑了摄动对最优值的影响,而没有考虑摄动对最优策略的影响,本文将讨论具有摄动的非平衡平均马氏均策规划和连续时间折扣马氏决策规划。     

DEA中连续C~2R模型理论的研究

在DEA中的C2R模型的基础上,针对决策单元输入与输出为[0,1]区间上的连续函数,建立了在一个时间区间内评价决策单元间的相对有效性的连续C2R模型以及其对偶模型,同时给出了决策单元的效率定义和弱DEA有效、DEA有效的定义.同时得到了弱对偶定理,从而初步构建了连续C2R模型的理论体系.     

权有附加约束的条件下的DEA有效性(C2R或C2GS2)

有关判别决策单元在权有附加约束的条件下是否DEA有效（C^2或C^2GS^2)，本文给出了一种基于权有附加约束条件下的加性模型的不同于文献[1]与[2]的约束与差别法。     

一种基于虚拟决策单元的排序方法的完善和扩展

本文对文[1]中提出的基于虚拟决策单元的排序方法进行了完善和扩展。首先,根据CCR模型,给出了两类特殊的DEA模型,分别是仅有投入数据的DEA模型和仅有产出数据的DEA模型;其次,基于这两个模型,应用上述方法实现了对仅有投入(或产出)数据的决策单元的排序;第三,给出了排序方法中参数a的计算方法;最后,通过修正排序模型,有效提高了排序方法的计算精度。改进后的排序方法避免了两个决策单元因为相对效率值过小而不能排序的情形,其应用范围也进一步扩大。     

关于DEA有效性“新方法”的探讨

主要指出文献[1],[2]中所用的"新方法"不能完全区分决策单元的DEA有效性和弱DEA有效性.同时,"新方法"中所使用的DEA模型(即文献[3]中超效率DEA模型)的最优解不一定存在,这也是"新方法"使用中的一大缺陷.本文同时指出"新方法"虽然是可以扩充的,但扩充后,某些"新模型"仍然会出现上述问题.如果单纯的去评价决策单元的DEA有效性、弱DEA有效性和非弱DEA有效性时,建议还是使用传统的经典模型为好;如果需要进一步对DEA有效性再进行分析,是可以象最早提出超效率DEA模型的文献[3]中那样去应用超效率DEA模型。     

关于几种三角形板元等价性的注记

1．引言求解薄板弯曲问题的广义协调元法近年来有了发展,本文讨论几种三角形板元之间的等价关系．我们证明,[2]中构造的GCⅢ－T9元等价于Specht元问．同一作者在[4]中构造的GCⅡ－T9元实际上也等价于Specht元,因此,它们彼此等价．另外,[7]中用对称列式构造的一个广义协调元是和作者在问中所引进的单元等价．例已指出,[7]中的那个元等价于问中的VZ1元,所以[7]和[6]中的两个广义协调元均等价于已知的VZ1元．2．广义协调GCⅢ－T9单元设三角形单元K的三个顶点依反时针方向分别为p i（xi,yi）,节点参数是pi点处的函数值及其一阶导…     

基于锥模型的一般信赖域算法收敛性分析

本文给出了锥模型信赖域算法的一般模型，它不仅包含通常的信赖域算法一相当于锥模型算法中bk＝0的情形，而且文献[1]的算法也可看作其子类．我们研究这个模型的较强的全局收敛性，并讨论保证算法具有超线性收敛速率的条件，从而推广了文[1]和文[4]中的若干结果．     

动态风险型的奥斯顿保险经济价值模型

Houston模型[1]没有风险分析,魏力仁[2]将他推广到风险分析的情况,并从两个角度对保险费率的取值进行了讨论。本文在[2]的基础上将Houston模型推广到动态的情形。Houston模型已被经济发达国家的企业采纳作为投保决策的参考依据。随着经济改革深入发展,我国企业也将面临一个经营投保决策问题。所以Houstort模型的研究有着它的现实意义。     

DEA中有效值的一种求法与保序的条件

对DEA中决策单元的有效值,本文给出了求它的二个定理,并给出了在导入新的决策单元后其保序的充分条件,最后举例说明这条件不成立时的结果.     

混合的DEA模型最优解的存在性

有ｎ个决策单元。设被评价的决策单元可以不是这ｎ个之一,且它们的输入或输出可以取负值,在这样情况下,给出了混合的ＤＥＡ模型存在最优解的必要条件或充分条件     

技术有效的决策单元与DEA有效性(C~2GS~2)

对李光金、阎洪先生所定义的技术有效的决策单元,证明了它是DEA有效(C~2GS~2)的,而且讨论了将非有效的决策单元转变为有效.     

On finding the most BCC-efficient DMU: A new integrated MIP–DEA model

This paper proposes a new integrated mixed integer programing – data envelopment analysis (MIP–DEA) model to improve the integrated DEA model which was introduced by Toloo & Nalchigar [M. Toloo, S. Nalchigar. A new integrated DEA model for finding most BCC–efficient DMU. Appl. Math. Model. 33 (2009) 597–60]. In this study some problems of applying Toloo & Nalchigar’s model are addressed. A new integrated MIP–DEA model is then introduced to determine the most BCC-efficient decision making unit (DMU). Moreover, it is mathematically proved that the new model identifies only a single BCC-efficient DMU by a common set of optimal weights. To show applicability of proposed models, a numerical example is used which contains a real data set of nineteen facility layout designs (FLDs).     

A new integrated DEA model for finding most BCC-efficient DMU

In many applications of widely recognized technique, DEA, finding the most efficient DMU is desirable for decision maker. Using basic DEA models, decision maker is not able to identify most efficient DMU. Amin and Toloo [Gholam R. Amin, M. Toloo, Finding the most efficient DMUs in DEA: an improved integrated model. Comput. Ind. Eng. 52 (2007) 71–77] introduced an integrated DEA model for finding most CCR-efficient DMU. In this paper, we propose a new integrated model for determining most BCC-efficient DMU by solving only one linear programming (LP). This model is useful for situations in which return to scale is variable, so has wider range of application than other models which find most CCR-efficient DMU. The applicability of the proposed integrated model is illustrated, using a real data set of a case study, which consists of 19 facility layout alternatives.     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

A distance friction minimization approach in data envelopment analysis: A comparative study on airport efficiency

This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving projection model, for both input reduction and output increase. In this approach, a generalized distance function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional projection function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner.     

Super-efficiency in DEA by effectiveness of each unit in society

One of the most important topics in management science is determining the efficiency of Decision Making Units (DMUs). The Data Envelopment Analysis (DEA) technique is employed for this purpose. In many DEA models, the best performance of a DMU is indicated by an efficiency score of one. There is often more than one DMU with this efficiency score. To rank and compare efficient units, many methods have been introduced under the name of super-efficiency methods. Among these methods, one can mention Andersen and Petersen’s (1993) [1] super-efficiency model, and the slack-based measure introduced by Tone (2002) [4]. Each of the methods proposed for ranking efficient DMUs has its own advantages and shortcomings. In this paper, we present a super-efficiency method by which units that are more effective and useful in society have better ranks. In fact, in order to determine super-efficiency by this method, the effectiveness of each unit in society is considered rather than the cross-comparison of the units. To do so, we divide the inputs and outputs into two groups, desirable and undesirable, at the discretion of the manager, and assign weights to each input and output. Then we determine the rank of each DMU according to the weights and the desirability of inputs and outputs.     

基于SMAA和公共权重的决策单元效率评价与排序

在数据包络分析(DEA)中,公共权重模型是决策单元效率评价与排序的常用方法之一。与传统DEA模型相比,公共权重模型用一组公共的投入产出权重评价所有决策单元,评价结果往往更具有区分度且更为客观。本文考虑决策单元对排序位置的满意程度,提出了基于最大化最小满意度和最大化平均满意度两类新的公共权重模型。首先,基于随机多准则可接受度分析(SMAA)方法,计算出每个决策单元处于各个排名位置的可接受度;然后,通过逆权重空间分析,分别求得使最小满意度和平均满意度最大化的一组公共权重;最后,利用所求的公共权重,计算各决策单元的效率值及相应的排序。算例分析验证了本文提出的基于SMAA的公共权重模型用于决策单元效率评价与排序的可行性。