Epsilon efficiency

This paper considers the extension of -optimality for scalar problems to vector maximization problems, or efficiency problems, which havem objective functions defined on a set .It is shown that the natural extension of the scalar -optimality concepts [viz, given >0, given a solution setS, ifxS there exists an efficient solutiony with f(x)–f(y), and given an efficient solutiony, there exists anxS with f(x)–f(y)] do not hold for some methods used. Six concepts of -efficient sets are introduced and examined, to a very limited extent, in the context of five methods used for generating efficient points or near efficient points.In doing so, a distinction is drawn between methods in which the surrogate optimizations are carried out exactly, and those where terminal -optimal solutions are obtained.The author would like to thank the referees whose thoroughness was extremely helpful for the revised paper.     

时间效益分析法在教学质量评价中的应用

文章在回顾教学质量评价方法的基础上 ,介绍了时间效益分析方法的基本原理并应用此方法 ,利用同一地区两所学校 95年中考成绩和 98年高考成绩对两所学校的教学质量进行了分析比较。文章最后还采用齐次马尔可夫链分析法和协方差分析方法对这两所学校的教学质量进行了评价 ,三种方法得出了相同的结论 ,从而验证了时间效益分析方法的可行性     

Pseudolinearity and efficiency

First order and second order characterizations of pseudolinear functions are derived. For a nonlinear programming problem involving pseudolinear functions only, it is proved that every efficient solution is properly efficient under some mild conditions.     

On value efficiency

Value efficiency analysis (VEA) is a data envelopment analysis (DEA)-based approach that measures the efficiency of decision-making units, incorporating the decision maker's preferences explicitly. If the functional form of the value function is assumed pseudoconcave, then a tangent cone where the most preferred point is its vertex can be used to recognize value inefficient points. In this article, we consider the value function assumptions and show that the pseudoconcavity assumption can be extended to also cover nonsmooth value functions in VEA using a known class of limiting subdifferentials in nonsmooth analysis. The focus of this article is to show that the tangent cone approach to recognize value inefficient points is a valid approach even if the value function assumptions are more general than pseudoconcavity. Moreover, we show that continuity is needed in the case of true value efficiency.     

Multi-directional efficiency analysis of efficiency patterns in Chinese banks 1997–2008

DEA-type efficiency studies are often used to investigate levels of efficiencies, differences in those levels between subgroups within a data set and possible determinants of such differences. In the current paper we show how differences in the efficiency patterns between different subgroups within a data set can be investigated using the more recent MEA methodology.     

Semi-radial technical efficiency measurement

Semi-radial efficiency measurement combines technical efficiency, as captured by the classical Farrell measure, with an economically meaningful mix efficiency component. The semi-radial evaluation we propose proceeds in two steps. First, we build on the price interpretation of the generally accepted Koopmans efficiency notion to characterize appropriate benchmarks. Next, we present both a quantity-based distance measure and its dual (price-based) equivalent to evaluate the mix efficiency factor. The type of measures we propose may, e.g., be used to provide a price rationale for the Zieschang technical efficiency evaluation procedure.     

Concepts of proper efficiency

The centrol concept of proper efficiency has been largely that of Geoffrion. There are, however, other concepts, and this paper considers two of them, viz. those of Klinger and Kuhn and Tucker, in relationship to each other and to Geoffrion. This is done in terms of various properties which characterise the efficient sets. Geoffrion's concept is a global one, whereas the other two concepts are local ones, and their significance is somewhat different. This is examined specifically in the context of optimal solutions, where, for example, it is shown that Geoffrion and Kuhn and Tucker proper efficiency fails to meet an optimality condition, which is satisfied by Klinger proper efficiency.     

Aggregation of scale efficiency

In this article we generalize the aggregation theory in efficiency and productivity analysis by deriving solutions to the problem of aggregation of individual scale efficiency measures, primal and dual, into aggregate primal and dual scale efficiency measures of a group (e.g., industry). The new aggregation result is coherent with aggregation framework and solutions that were earlier derived for other related efficiency measures and can be used in practice for estimation of scale efficiency of an industry or other groups of firms within it.     

Optimality and efficiency I

Given a set of alternatives, X and a set of value, or utility, functions, V, on X, contemporary work in the Decision Theory field deals with the reduction of X to some acceptable subset Y. This paper deals with the various ways in which this may be done, more specifically with the optimal set, M(X, V), the efficient set E(X, V) and efficient sets ?(X, f), ?(X, f), ?(X, f), when the value of an alternative can be expressed in terms of a multi-objective vector f on X. Relationships between these various sets are explained. The importance of the differences and similarities is seen to depend on the nature of the circumstances faced by the decision analyst at each stage of the evolutionary process of analysis, and upon their use for computational purposes. Some contemporary work (e.g. portfolio analysis) is examined within this framework.     

Microfinance in Sub-Saharan Africa: social efficiency,financial efficiency and institutional factors

Central European Journal of Operations Research - There are two natural efficiency measures associated with microfinance banking: social efficiency, measuring to what extent the micro-capital...     

The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models

The infeasibility problem in traditional super efficiency models has been well established. A generalization of traditional input- or output-oriented super efficiency models, the directional distance function also suffers from infeasibility and related problems. The hyperbolic-oriented efficiency measure provides an alternative to the input-oriented, output-oriented, and directional efficiency measures in super efficiency models and it has the distinct advantage of eliminating the infeasibility problem for positive input/output data. We also show that using a hyperbolic orientation in a super efficiency model allows us to find feasible solutions for certain cases when the requirement for all data to be positive is relaxed. Further we demonstrate the hyperbolic orientated super efficiency method in an outlier detection application. Together, these results establish the use of the hyperbolic orientation in super efficiency analysis as a realistic alternative in practice.     

Measuring the efficiency of NBA teams: additive efficiency decomposition in two-stage DEA

This paper evaluates the efficiency of National Basketball Association (NBA) teams under a two-stage DEA framework. Applying the additive efficiency approach, we decompose overall team efficiency into first-stage wage efficiency and second-stage on-court efficiency and find out the individual endogenous weights for each stage. The empirical results show that NBA teams present a better performance on wage efficiency than for on-court efficiency, as on-court efficiency is influenced by many uncontrollable factors. Moreover, NBA teams, on average, tend to possess a higher weight on the first stage, suggesting that teams’ managers can enhance organizational efficiency more efficaciously by prudentially recruiting players.     

Technical efficiency and economies of scale: A non-parametric analysis of REIT operating efficiency

This study measures technical efficiency and economies of scale for real estate investment trusts (REITs) by employing data envelopment analysis (DEA), a linear-programming technique. Using data from the National Association of Real Estate Investment Trusts (NAREITs) for the years 1992–1996, we find that REITs are technically inefficient, and the inefficiencies are a result of both poor input utilization and failure to operate at constant returns to scale. With respect to scale inefficiency, most REITs are operating at increasing returns to scale, suggesting that REITs could improve performance through expansion. Moreover, we employ regression analysis to determine what characteristics influence the efficiency measures obtained. The results show that internal REIT management is positively related to all measures of efficiency. Increasing leverage is negatively related to REIT input utilization. Finally, increasing REIT diversification across property types enhances scale efficiency (SE) but reduces input usage efficiency.     

Social efficiency in microfinance institutions

Microfinance institutions (MFIs) are a special case in the financial world. They have a double financial and social role and need to be efficient at both. In this paper, we try to measure the efficiency of MFIs in relation to financial and social outputs using data envelopment analysis. For the analysis of financial efficiency, we rely on existing literature for traditional financial institutions. To this we have added two indicators of social performance: impact on women and a poverty reach index. We have studied the relationship between social and financial efficiency, and the relationship between efficiency and other indicators, such as profitability. Other aspects studied are the relation between social efficiency and type of institution—Non-Governmental Organization (NGO)—, non-NGO, and the importance of geographical region of activity. The results reveal the importance of social efficiency assessment.     

Higher-order conditions for strict efficiency

Luu and Kien (On higher order conditions for strict efficiency, Soochow J. Math. 33 (2007), pp. 17–31), proposed higher-order conditions for strict efficiency of vector optimization problems based on the derivatives introduced in Ginchev (Higher order optimality conditions in nonsmooth optimization, Optimization 51 (2002), pp. 47–72). These derivatives are defined for scalar functions and in their terms necessary and sufficient conditions are obtained a point to be strictly efficient (isolated) minimizer of a given order for quite arbitrary scalar function. Passing to vector functions, Luu and Kien lose the peculiarity that the optimality conditions work with arbitrary functions. In this article, applying the mentioned derivatives for the scalarized problem and restoring the original idea, optimality conditions for strict efficiency of a given order are proposed, which work with quite arbitrary vector functions. It is shown that the results of Luu and Kien are corollaries of the given conditions and generalizations are discussed.     

Undesirable outputs in efficiency valuations

Efficiency measurement is usually based on the assumption that inputs have to be minimized and outputs have to be maximized. In a growing number of applications, however, undesirable outputs are incorporated into the production model which have to be minimized. In this paper various approaches for treating such outputs in the framework of Data Envelopment Analysis (DEA) are discussed and the resulting efficient frontiers are compared. New radial measures are introduced which assume that any change of the output level will involve both undesirable and desirable outputs.     

On semigroup presentations and efficiency

The purpose of this paper is twofold. First we determine some forms of the relations in a finite semigroup presentation with zero deficiency which does or does not define a group. Moreover, we conclude that a finite Rees matrix semigroup M [G; I, Λ; P] is efficient when G is efficient and the index sets I, Λ are finite.     

An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

In DEA, we have two measures of technical efficiency with different characteristics: radial and non-radial. In this paper we compile them into a composite model called “epsilon-based measure (EBM).” For this purpose we introduce two parameters which connect radial and non-radial models. These two parameters are obtained from the newly defined affinity index between inputs or outputs along with principal component analysis on the affinity matrix. Thus, EBM takes into account diversity of input/output data and their relative importance for measuring technical efficiency.