模糊非径向DEA模型的可信度求解

传统的DEA模型(CCR、BCC)的径向效率度量是不完全的.它们只是分别地度量输入效率与输出效率,且效率度量没有考虑非零的输入松弛与输出松弛.修正的Russell方法消除了这些缺陷.基于修正的Russell方法,利用可信度方法,模糊DEA模型得以建立并求解.一个算例佐证了这一方法.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

Measure based representation of uncertain information

We discuss the use of monotonic set measures for the representation of uncertain information. We look at some important examples of measure-based uncertainty, specifically probability and possibility and necessity. Others types of uncertainty such as cardinality based and quasi-additive measures are discussed. We consider the problem of determining the representative value of a variable whose uncertain value is formalized using a monotonic set measure. We note the central role that averaging and particularly weighted averaging operations play in obtaining these representative values. We investigate the use of various integrals such as the Choquet and Sugeno for obtaining these required averages. We suggest ways of extending a measure defined on a set to the case of fuzzy sets and the power sets of the original set. We briefly consider the problem of question answering under uncertain knowledge.     

Additive DEA based on MCDA with imprecise information

This work exploits links between Data Envelopment Analysis (DEA) and multicriteria decision analysis (MCDA), with decision making units (DMUs) playing the role of decision alternatives. A novel perspective is suggested on the use of the additive DEA model in order to overcome some of its shortcomings, using concepts from multiattribute utility models with imprecise information. The underlying idea is to convert input and output factors into utility functions that are aggregated using a weighted sum (additive model of multiattribute utility theory), and then let each DMU choose the weights associated with these functions that minimize the difference of utility to the best DMU. The resulting additive DEA model with oriented projections has a clear rationale for its efficiency measures, and allows meaningful introduction of constraints on factor weights.     

The extension and integration of the inverse DEA method

The inverse DEA (Data Envelopment Analysis) method is primarily used to analyse the changing relationship between the inputs and outputs of a DMU (Decision-Making Unit) when its efficiency is kept constant or set to a target value. However, the existing inverse DEA method cannot be applied directly to estimate all the changing relationships. For example, the existing DEA models fail to estimate the input variations when the supervisor wants to maintain the DMU’s output-oriented efficiency during the downscaling of production. This paper analyses all the possible changing relationships that need to be solved by the inverse DEA method and develops different models for both the output and input orientations, accomplishing the extension and integration of the inverse DEA model. For illustration of our results, a numerical example is given.     

The overall efficiency of the dynamic DEA models

Central European Journal of Operations Research - This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA...     

Centralized resource allocation DEA models based on revenue efficiency under limited information

In this paper, we extend the centralized DEA models by Lozano et al (2011) to allocate resources based on revenue efficiency across a set of DMUs under a centralized decision-making environment. The aim is to allocate resources so as to maximize the total output revenue produced by all the DMUs under limited information. To uncover the sources of total revenue increase from the centralized resource allocation model, we further decompose the aggregate revenue efficiency into three components: the aggregate output-oriented technical efficiency, the aggregate output allocative efficiency and the aggregate revenue re-allocative efficiency. Finally, two empirical data sets are presented to show that our proposed approach is not only an efficient tool to allocate the resources among the DMUs based on the revenue efficiency but additionally provides the central DM with guidance on how to identify the weak areas where more effort should be devoted to improve the total outputs.     

Optimal portfolio strategies benchmarking the stock market

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.     

An independent benchmarking of SDP and SOCP solvers

 This work reports the results of evaluating all computer codes submitted to the Seventh DIMACS Implementation Challenge on Semidefinite and Related Optimization Problems. The codes were run on a standard platform and on all the benchmark problems provided by the organizers of the challenge. A total of ten codes were tested on fifty problems in twelve categories. For each code the most important information is summarized. Together with the tabulated and commented benchmarking results this provides an overview of the state of the art in this field. Received: March 27, 2001 / Accepted: April 5, 2002 Published online: October 9, 2002 Key Words. semidefinite programming – second order cone programming – optimization software – performance evaluation This work is supported in part by grant NSF-CISE-9981984     

集合保单不同质性的度量指标

针对保险索赔次数数据,本文基于混合Poisson分布研究了保险中集合保单不同质性的度量方法;给出不同质性系数的定义、估计方法及实例。     

数据包络分析在信用评估中的应用

提出了一种基于拒绝案例集的数据包络分析模型和边界为分段线性分离超平面的分类方法，探讨了在只掌握单方面信息(信用差的单位)的情况下，如何对新单位进行信用评估的问题，并给出了评价决策单元信用状况的具体方法，应用实例表明所提出的模型和方法是可行的。     

测度的微分同测度与单位逼近的卷积的边界渐近性质

文中对通常意义下的核与定义在RN上的有限Borel测度μ作卷积之后得到的u加以讨论,研究了u在边界Arn+1+处的渐近性质.根据μ的对称导数与的性质,得到了同N.A.Watson类似的结果,也就是本文的主要结果.即:当μ为正测度时,u(x,t)(t→0)与μ的对称导数是相互等价的.并由此将N.A.Watson的结果加以推广.     

The Pointwise Densities of the Cantor Measure

Let be the classical middle-third Cantor set and let μ be the Cantor measure. Set s = log 2/log 3. We will determine by an explicit formula for every point x the upper and lower s-densities Θ*^s(μ , x), Θ*^s(μ , x) of the Cantor measure at the point x, in terms of the 3-adic expansion of x. We show that there exists a countable set F such that 9(Θ*^s(μ , x))^{− 1/s} + (Θ*^s(μ , x))^{− 1/s} = 16 holds for x \F. Furthermore, for μ_C almost all x, Θ*^s(μ , X) − 2 · 4^{− s} and Θ*^s(μ , x) = 4^{− s}. As an application, we will show that the s-dimensional packing measure of the middle-third Cantor set is 4^s.     

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。     

人口对区域可持续发展的影响的DEA分析

探讨将DEA方法用于区域社会经济可持续发展的人口条件问题分析，提出了完全投入冗余率的概率，并以广东省为例，定量地揭示了人口数量条件对区域社会经济可持续发展的影响以及人口数量控制的具体目标值。     

满Parry测度的有限型子集的Hausdorff维数与测度

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.     

DEA方法在卫生经济学中的应用

自八十年代中期以来 ,对医院和医疗卫生系统进行效率评估引起了人们的广泛关注 ,越来越多的学者开始从事这一领域的研究 .数据包络分析方法 ( DEA)因其可对多输入 ,多输出的系统进行综合效率评价 ,这一特性正符合医院和医疗卫生系统中具有多投入和多产出的特点 ,从而在医院和医疗卫生系统的效率评估中受到重视并有着重要应用 .本文综述了现有文献中有关 DEA方法在医院和医疗卫生系统效率评估的应用 ,对已得到应用的 DEA模型作了简单的介绍 ,同时对 DEA模型和方法的进一步应用给出了建议 .     

The LeChatelier principle in a DEA model

This paper aims to relate the LeChatelier principle, first introduced into economics by Samuelson (1947), with the DEA approach through two propositions. These propositions allow for bridging the principle over a DEA model with and without the presence of non-discretionary inputs and enable one to make comparisons for the various efficiency measures under different conditions. The quasi-fixity of some inputs hinders a firm’s capacity from instantly and freely adjusting its input combination in order to minimize its production costs. The assumption that all inputs are discretionary tends to exaggerate managers’ ability to dispense resources and renders invalid information on the adjustment of the current input mix.