考虑指标关联的网络DEA效率测度研究

现有网络DEA模型通常在测度指标相互独立的假设前提下进行生产系统效率测度,然而这一假设并不与现实完全相符.针对网络生产系统效率测度指标间存在关联关系的情形,引入模糊测度理论中的Choquet积分,对传统网络DEA模型进行了扩展·首先,分别给出了Choquet积分和网络DEA模型的相关基础知识;然后以串联DEA模型为例,构建了考虑指标间关联的网络DEA模型(C-NDEA模型),进而定义了指标关联情形下网络生产系统有效性的判定标准,并给出了相关定理及其证明;最后通过一个算例验证了所构建C-NDEA模型的合理性和有效性.     

引入时间变量的数据包络分析模型

考虑到实际中的生产过程大多数都是多阶段的生产过程,而传统的数据包络分析模型只能对单阶段的生产过程进行评价.传统的数据包络分析模型在应用中的局限性很大.本文是在传统数据包络分析模型的基础上,通过引入离散的时间变量来建立对整个多阶段生产过程进行评价的数据包络分析模型.     

Efficiency bounds in Data Envelopment Analysis

This paper considers a proposal, by Chang and Guh, that the non-archimedean infinitesimal in the CCR data envelopment analysis model be replaced with a data-dependent finite magnitude. Whilst the intention of the proposal is clear: to reduce the CCR efficiency rating of certain problematic DMUs, it is found not to work in practice. An alternative implementation, which puts the CCR model into a mixed-binary linear programming framework, is developed. Chang and Guh's proposal is also related to the earlier modification to the CCR model, Constrained Facet Analysis. Both are seen as providing bounds on the relative efficiency of DMUs which are not properly enveloped in the CCR model.     

The Potential for Endogeneity Bias in Data Envelopment Analysis

Data envelopment analysis has become an important technique for modelling the relationship between inputs and outputs in the production process, particularly in the public sector. However, whenever measures of the output of public sector activity receive public attention, there is a strong possibility that there will be a feedback from the achieved output to the resources devoted to the activity. In other words, the level of resources is endogenous. The implications of such endogeneity for standard econometric estimation techniques are well known, and methods exist to deal with the problem. Most commentators have assumed that endogeneity poses no analogous problems for DEA because the technique merely places an envelope around feasible production possibilities. Using Monte Carlo simulation techniques, however, this paper shows that the efficiency estimates generated by DEA in the presence of endogeneity can be subject to bias, in the sense that inefficient units using low levels of the endogenous resource may be set tougher efficiency targets than equally inefficient units using more of the resource, particularly when sample sizes are small. The paper concludes that, in such circumstances, great caution should be exercised when comparing efficiency measures for units using different levels of the endogenous input.     

Data Envelopment Analysis with Preference Structure

It is important to consider the decision making unit (DMU)'s or decision maker's preference over the potential adjustments of various inputs and outputs when data envelopment analysis (DEA) is employed. On the basis of the so-called Russell measure, this paper develops some weighted non-radial CCR models by specifying a proper set of ‘preference weights’ that reflect the relative degree of desirability of the potential adjustments of current input or output levels. These input or output adjustments can be either less or greater than one; that is, the approach enables certain inputs actually to be increased, or certain outputs actually to be decreased. It is shown that the preference structure prescribes fixed weights (virtual multiplier bounds) or regions that invalidate some virtual multipliers and hence it generates preferred (efficient) input and output targets for each DMU. In addition to providing the preferred target, the approach gives a scalar efficiency score for each DMU to secure comparability. It is also shown how specific cases of our approach handle non-controllable factors in DEA and measure allocative and technical efficiency. Finally, the methodology is applied with the industrial performance of 14 open coastal cities and four special economic zones in 1991 in China. As applied here, the DEA/preference structure model refines the original DEA model's result and eliminates apparently efficient DMUs.     

模糊数据包络分析方法有效性分析

传统数据包络分析(DEA)模型只能用来评价具有精确投入和产出数据的决策单元.然而在实践中决策单元的投入产出数据可能存在一定模糊性.为了评价具有模糊投入产出数据的决策问题,研究工作者提出了模糊数据包络分析模型,并给出了相应的有效性定义.对于不同研究者提出的有效性定义方式有众多地方需要改进.通过这些改进提出了相关模型及新的有效性定义方式,并给出了相关实例.     

Data Envelopment Analysis of multiple response experiments

Taguchi method is the usual strategy in robust design and involves conducting experiments using orthogonal arrays and estimating the combination of factor levels that optimizes a given performance measure, typically a signal-to-noise ratio. The problem is more complex in the case of multiple responses since the combinations of factor levels that optimize the different responses usually differ. In this paper, an Artificial Neural Network, trained with the experiments results, is used to estimate the responses for all factor level combinations. After that, Data Envelopment Analysis (DEA) is used first to select the efficient (i.e. non-dominated) factor level combinations and then for choosing among them the one which leads to a most robust quality loss penalization. Mean Square Deviations of the quality characteristics are used as DEA inputs. Among the advantages of the proposed approach over traditional Taguchi method are the non-parametric, non-linear way of estimating quality loss measures for unobserved factor combinations and the non-parametric character of the performance evaluation of all the factor combinations. The proposed approach is applied to a number of case studies from the literature and compared with existing approaches.     

一类基于属性变量的DEA模型

系统评价不仅应重视系统的经济特征,还必须重视系统的非经济特征.在评价系统的非经济特征时必须考虑属性变量,即不能以货币衡量的反映系统非经济特征的定量变量.在过去关于DEA的研究中并未涉及到这种变量.本文对属性变量进行了明确的定义,并提出一种基于属性变量的DEA效率评价模型,最后通过实例演示了模型的合理性.     

Fuzzy BCC Model for Data Envelopment Analysis

Fuzzy Data Envelopment Analysis (FDEA) is a tool for comparing the performance of a set of activities or organizations under uncertainty environment. Imprecise data in FDEA models is represented by fuzzy sets and FDEA models take the form of fuzzy linear programming models. Previous research focused on solving the FDEA model of the CCR (named after Charnes, Cooper, and Rhodes) type (FCCR). In this paper, the FDEA model of the BCC (named after Banker, Charnes, and Cooper) type (FBCC) is studied. Possibility and Credibility approaches are provided and compared with an -level based approach for solving the FDEA models. Using the possibility approach, the relationship between the primal and dual models of FBCC models is revealed and fuzzy efficiency can be constructed. Using the credibility approach, an efficiency value for each DMU (Decision Making Unit) is obtained as a representative of its possible range. A numerical example is given to illustrate the proposed approaches and results are compared with those obtained with the -level based approach.     

Restricting Weight Flexibility in Data Envelopment Analysis

In this paper we present a method, based on the use of proportions, for restricting weight flexibility in data envelopment analysis. This method is applicable when the decision-making units being evaluated have multiple inputs and outputs.     

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.     

On the Use of Ordinal Data in Data Envelopment Analysis

In many problems involving efficiency analysis using DEA, certain factors may be measurable only on an ordinal scale. Specifically, it may be possible only to rank order the DMUs according to a factor, rather than being able to assign a specific numerical value of that factor to each DMU. To illustrate this, we examine a problem involving the evaluation of new technology installations. The presence of qualitative factors in such an environment motivates the need to investigate how such factors can be incorporated into existing efficiency measurement models. In particular, a procedure is presented for incorporating an ordinal factor into the DEA structure, with the resulting formulation being a particular form of cone ratio model. The model is then applied to the technology installation efficiency problem.     

Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis

We contrast the different approaches of Data Envelopment Analysis (DEA) and Multiple Criteria Decision Making (MCDM) to superficially similar problems. The concepts of efficiency and Pareto optimality in DEA and MCDM are compared, and a link is demonstrated between the ratio efficiency definition in DEA and a distance measure in input–output space based on linear value functions. The problem of weight sensitivity is discussed in terms of value measurement theory, highlighting the assumptions needed during model formulation in order to justify the use of value judgements to constrain weight flexibility in DEA. Finally, we propose a stochastic approach, in which a probability distribution on efficiencies can be derived for each decision making unit, as a basis for comparison.     

The Efficiency Distribution Approach in Data Envelopment Analysis: An Application

A method is developed here for characterizing the empirical distribution of the efficient units in data envelopment analysis. Two empirical applications illustrate the various uses of the distribution approach. One involves the cost frontier which exhibits increasing returns to scale and the other involves a dynamic production frontier, where technological change causes a shift of the production frontier over time.     

基于数据包络分析的模糊综合评价方法

提出基于数据包络分析的模糊综合评价方法.在该方法中,对于综合评价体系中的量化指标,采用数据包络分析方法得到各评价单元的相对效率,再对相对效率进行模糊化计算,并与非量化指标一起进行模糊综合评价.利用数据包络分析的优化结果代替模糊评价中的专家评分,使模糊综合评价更具客观说服力,为一类既有客观数据,又有主观因素的复杂系统的综合评价提供新的研究思路.最后,采用该方法对出入境检验检疫系统的8个实验室进行综合评价.     

BiLevel programming Data Envelopment Analysis with constrained resource

A new BiLevel programming Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the performance of a system with Stackelberg-game relationships. This new approach allows us to evaluate the firm performance in decentralized decisions, which consist of the objective(s) of the leader at its first level and that is of the follower at the second level. This approach can help decentralized companies to optimize their performance using multiple inputs to produce multiples outputs in a cost-effective way, where both the system “black-box” and subsystem performance are exposed in details. We show the algorithms and solutions to our new models. We illustrate and validate the proposed new approach using two case studies: a banking chain and a manufacturing supply chain. The computation shows that subsystem being efficient at all levels results in an overall efficiency achievement in a decentralized BiLevel structure.     

A Semi-Infinite Programming Model In Data Envelopment Analysis

We consider a model for data envelopment analysis with infinitely many decision-making units. The determination of the relative efficiency of a given decision-making unit amounts to the solution of a semi-infinite optimization problem. We show that a decision-making unit of maximal relative efficiency exists and that it is 100% efficient. Moreover, this decision-making unit can be found by calculating a zero of the semi-infinite constraint function. For the latter task we propose a bi-level algorithm. We apply this algorithm to a problem from chemical engineering and present numerical results