Gradual technical and scale efficiency improvement in DEA

In data envelopment analysis (DEA) an inefficient unit can be projected onto an efficient target that is far away, i.e. reaching the target may demand large reductions in inputs and increases in outputs. When the inputs and outputs modifications planned are large, it may be troublesome to carry them out all at once. In order to help an inefficient unit reach a distant target, a strategy of gradual improvements with successive, intermediate targets has been proposed. This paper extends such approach to the variable returns to scale (VRS) case. In the VRS scenario we distinguish between units that are technical efficient and those that are not. On the one hand, for those units that are not technical efficient the proposed approach determines successive intermediate targets leading to the technical efficiency frontier, i.e. the priority for those units is to attain technical efficiency. On the other hand, for those units that are technical efficient but not scale efficient the proposed approach computes a sequence of targets ending in the global efficiency frontier, i.e. when technical efficiency is guaranteed the goal is then to attain global efficiency. In both cases, the successive targets are obtained by iteratively solving specific DEA models that take into account given bounds on the rates of change in inputs and outputs that the unit can implement in each step.     

Generalized sensitivity indices based on vector projection for multivariate output

Analyzing the sensitivity of model outputs to inputs is important to assess risk and make decisions in engineering application. However, for model with multiple outputs, it is difficult to interpret the sensitivity index since the effect of the dimension and the correlation between multiple outputs are often ignored in the existing methods. In this paper, a new kind of sensitivity analysis method is proposed by use of vector projection and dimension normalization for multiple outputs. Through the dimension normalization, the space of multiple outputs can be unified into a dimensionless one to eliminate the effect of the dimension of the different output. After an affine coordinate system is constructed by considering the correlation of the multiple normalized outputs, a total variance vector for the multiple outputs can be composed by the individual variance of each output. Then, by projecting the variance contribution vector composed by the individual variance contribution of the input to each output on the total variance vector, the new sensitivity indices are proposed for measuring the comprehensive effect of the input on the total variance vector of multiple outputs, it is defined as the ratio of the projection of the variance contribution vector to the norm of the total variance vector. We derive that the Sobol’ indices for a scalar output and the covariance decomposition based indices for multiple outputs are special cases of the proposed vector projection based indices. Then, the mathematical properties and geometric interpretation of the proposed method are discussed. Three numerical examples and a rotating shaft model of an aircraft wing are used to validate the proposed method and show their potential benefits.     

The effect of competition on the efficiency of secondary schools in England

In this paper we calculate the technical efficiencies, based upon multiple outputs – school exam performance and attendance rates – of all secondary schools in England over the period 1993–1998. We then estimate models to examine the determinants of efficiency in a particular year, and the determinants of the change in efficiency over the period. Our results suggest that the greater the degree of competition between schools the more efficient they are. The strength of this effect has also increased over time which is consistent with the evolution of the quasi-market in secondary education. Competition is also found to be an important determinant of the change in efficiency over time. There is, however, some evidence of conditional convergence between schools.     

A generalized inefficiency model with input and output dependence

In this paper we propose a general inefficiency model, in the sense that technical inefficiency is, simultaneously, a function of all inputs, outputs, and contextual variables. We recognize that change in inefficiency is endogenous or rational, and we propose an adjustment costs model with firm-specific but unknown adjustment cost parameters. When inefficiency depends on inputs and outputs, the firm's optimization problem changes as the first order conditions must take into account the dependence of inefficiency on the endogenous variables of the problem. The new formulation introduces statistical challenges which are successfully resolved. The model is estimated using Maximum Simulated Likelihood and an empirical application to U.S. banking is provided.     

系数为LR-型模糊数的模糊线性最小二乘回归

针对输入、输出以及系数为LR-型模糊数的情况,建立模糊线性回归模型,提出该模型的最小二乘估计以及模型性能评价方法。当输入、输出以及系数都退化为精确值时,该估计退化为经典的最小二乘估计。该方法不仅适用于三角模糊数,也适用于其它LR-型模糊数(如指数型模糊数)。数值模拟表明,该方法的拟合效果较好。     

Statistical approach to the code acquisition problem in direct-sequence spread-spectrum communication systems

^** Email: eshima{at}med.oita-u.ac.jp In direct-sequence spread-spectrum (DS/SS) communication, users'original signals are modulated into higher frequencies withthe users' codes. DS/SS communication has the attractive propertythat multiple users' signals can be simultaneously transmitted;however, communication cannot be performed without synchronizationof users' spread-spectrum (SS) signal. Synchronization is typicallyperformed in two steps, i.e. code acquisition and tracking.This paper gives a statistical solution to the question as tohow code acquisition can be performed effectively and precisely.First, properties of matched-filter outputs of SS signal arediscussed. Second, a theoretical method of code acquisitionis proposed according to statistical decision theory. The methoduses all matched-filter outputs for code acquisition. Third,matched-filter outputs are dichotomized with a threshold valueand the dichotomous outputs are used for code acquisition. Asimple and effective method for code acquisition is proposed.Numerical simulations are also given to illustrate the effectivenessof the proposed method. Finally, a further discussion and conclusionto this study are provided.     

Optimal Noise Rejection in Structural Analysis by Means of Generalized Sampled-Data Hold Functions

In this paper, a technique for optimal noise rejection, based on generalized sampled-data hold functions is applied to the control of civil engineering structures. The technique consists in suitably modulating the sampled outputs of the system under control by periodically varying functions in order to attenuate the effect of the disturbances on the system states to an acceptable level, by minimizing a quadratic cost function. This minimization is performed by feeding back the outputs of the system, which are assumed to be corrupted by measurement noise. Moreover, in the present paper, the robustness properties of the GSHF based optimal regulator is analyzed and guaranteed stability margins, expressed in terms of elementary cost and system matrices, are proposed for such a type of optimal regulators. The effectiveness of the method is demonstrated by various simulation results. The results of the paper can be used to assess the detrimental effect of noise on the closed-loop system and the tradeoff involved in assuring good sampled-data performance and sufficient robustness.     

Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs

The paper focuses upon situations in which decision-making units carry out their production activities with some inputs or outputs unobservable (or possibly omitted), and when there are a priori known constraints on the relative significance of otherwise observable (or explicitly considered) inputs and outputs. For such settings, the paper proposes a modification that alters traditional construction of the production possibility set and isolates the role of the unobservable (or omitted) variables in production by means of restrictions on virtual inputs and outputs being converted into production trade-offs. In effect, the proposed procedure induces unit-specific production possibility sets that derive from production trade-offs framed for units assessed separately to reflect their specific observed production conditions. The modification is implemented within a weighted slacks-based measure with restricted direction of slacks in order to make technical efficiency measurement more informative and consistent with the operating conditions under which production activities are accomplished. These ideas are illustrated and models implemented in a case study of bank branch performance measurement.     

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker’s value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data.     

Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output

China’s rapid development in economy has intensified many problems. One of the most important issues is the problem of environmental pollution. In this paper, a new DEA approach is proposed to measure the environmental efficiency of thermoelectric power plants, considering undesirable outputs. First, we assume that the total amount of undesirable outputs of any particular type is limited and fixed to current levels. In contrast to previous studies, this study requires fixed-sum undesirable outputs. In addition, the common equilibrium efficient frontier is constructed by using different input/output multipliers (or weights) for each different decision making unit (DMU), while previous approaches which considered fixed-sum outputs assumed a common input/output multiplier for all DMUs. The proposed method is applied to measure the environmental efficiencies of 30 thermoelectric power plants in mainland China. Our empirical study shows that half of the plants perform well in terms of environmental efficiency.

     

基于马氏距离的TOPSIS决策方法及其应用

针对决策指标之间的相关性问题,将马氏距离引入传统TOPSIS方法,提出了基于马氏距离的TOPSIS方法.在此基础上,分析了基于马氏距离改进后贴近度的性质,并以投资决策方案选择为例加以说明.结果表明,基于马氏距离改进的TOPSIS方法对决策数据的非奇异线性变换具有不变性.协方差矩阵体现了决策指标之间的相关性,因而可以有效避免指标的相关性对决策效果的影响.     

Improving data envelopment analysis by the use of production trade-offs

Production technologies in data envelopment analysis (DEA) are described in terms of inputs and outputs. Production trade-offs represent simultaneous changes to the inputs and outputs that are possible in the technology under consideration. Recently, a method for their incorporation in DEA models has been developed. It was shown that the use of production trade-offs not only improves the discrimination of DEA models but also preserves the traditional meaning of efficiency as a radial improvement factor for inputs and outputs. This new paper follows the above development and provides an example of its use in the assessment of efficiency of university departments. The paper avoids excessive technical detail which can be found in the previous publication and instead focuses on the implementation of this new technique.     

Optimization of probabilistic multiple response surfaces

Response surface methodology (RSM) is a statistical-mathematical method used for analyzing and optimizing the experiments. In analysis process, experts usually face several input variables having effect on several outputs called response variables. Simultaneous optimization of the correlated response variables has become more important in complex systems. In this paper multi-response surfaces and their related stochastic nature have been modeled and optimized by Goal Programming (GP) in which the weights of response variables have been obtained through a Group Decision Making (GDM) process. Because of existing uncertainty in the stochastic model, some stochastic optimization methods have been applied to find robust optimum results. At the end, the proposed method is described numerically and analytically.     

基于M-LSTM的股票指数日内交易量分布预测研究

针对现有预测建模方法难以高效提取日内交易量分布复杂变化规律,影响VWAP策略执行效果的问题,本文提出一种MEMD分解下基于LSTM-Attention的股市指数日内交易量分布预测方法M-LSTM。首先,运用MEMD方法将区间多维交易量时序同步分解为若干个独立的本征模态函数(IMF);其次,对各维度分解中高频IMF进行去噪与重构,构建基于LSTM-Attention神经网络的日内交易量分布预测模型,并深入分析股票指数不同走势阶段下模型预测的有效性;最后,分别采用M-LSTM、ARIMA以及SVR等主流方法,对上证指数等四个代表性指数的日内交易量分布进行预测。实验结果表明:M-LSTM预测误差更小,是一种更有效的股票指数日内交易量分布预测方法。     

Generating strong defining hyperplanes of the production possibility set in data envelopment analysis

In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperplanes determine the nature of returns to scale. The present work proposes a method for generating all linearly independent strong defining hyperplanes (LISDHs) of the PPS passing through a specific decision making unit (DMU). To this end, corresponding to each efficient unit, a perturbed inefficient unit will be defined and, using at most m+s linear programs, all LISDHs passing through the DMU will be determined, where m and s are the numbers of inputs and outputs, respectively.     

Technical change and the von Neumann coefficient of uniform expansion

We study technical change for multi-product technologies to examine its effect on economic growth for 27 OECD (Organization for Economic Cooperation and Development) countries during 1951–2014. We review the Malmquist index and reexamine von Neumann’s model of an expanding economy. We estimate the coefficient of uniform expansion via DEA (Data Envelopment Analysis) and use it to measure technical change via a Solow residual and an alternative von Neumann technical change index which equals the difference between the growth rates of the slowest growing output and the fastest growing input. We also exploit a property of constant returns to scale in order to examine technical change of the average technology. During 2005–2014 the Solow residual shows relatively fast technical change. In contrast, the Malmquist, average technology and alternative von Neumann technical change indexes show negative or stagnant technical change.     

Two-stage procedure of estimation of reliability indexes from forced and service tests

Prolonged experiments are needed to control the reliability of modern technical products. One method of their shortening is the use of tests under forced regimes. To interpret the results of forced tests with regard to normal conditions the relationship between reliability indexes (RI) and test regime is used. This relationship is determined from preliminary tests. In this approach the above mentioned relationship between RI and test regime is assumed to be valid for all batches of products. It is noted in [1] that the technical characteristics of products are random variables whose distributions depend on production conditions. Therefore for different batches RI may vary rather widely under the same conditions. In the present paper the model of dependence of RI on some inner product parameters instead of those of the testing regime is used to find the common relationship for different products. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 52–58, Perm, 1991.     

Reducing Weight Flexibility in Data Envelopment Analysis

This paper explores the consequences of total weight flexibility in data envelopment analysis (DEA) assessments of the efficiency of decision-making units, and it suggests one possible way of limiting such flexibility. It is suggested that total weight flexibility can lead to some decision-making units being assessed, in effect, on only a small subset of their inputs and outputs, while the rest of their inputs and outputs are all but ignored. Constraining the weights in DEA assessments overcomes this problem. The paper suggests one way in which constraints can be placed for the case where the decision-making units to be assessed use only a single input. The method is illustrated using data on local-authority rates departments. Finally, the paper discusses the interpretation and usefulness of the information obtained from DEA assessments involving weights constraints.     

基于两阶段DEA方法的中国商业银行效率评价

本文考虑商业银行吸收存款和发放贷款的两阶段特点,引入“顾客满意度”这一产出指标,应用两阶段DEA模型计算了我国15家商业银行在2008年和2011年的服务质量效率和盈利效率,结果显示我国商业银行的盈利效率显著高于服务质量效率。进而综合考虑服务和盈利指标,分析了各银行的综合效率,并通过计算各银行Malmquist指数研究我国商业银行2008年到2011年间的效率变化。结果表明:各商业银行从2008年到2011年的效率整体呈上升趋势,各商业银行的技术效率以及整个银行业的效率都有一定的提高。最后,应用Tobit模型分析了影响银行效率的因素,结果显示银行的贷存比、资产利润率和不良贷款率对效率影响显著。