Management of nursing homes using data envelopment analysis.

Data envelopment analysis (DEA) is used to evaluate the relative technical efficiency and assist in the management of a chain of nursing homes. As with any DEA model, variables chosen are particularly important. The study looks at two possibly critical issues. The first is the appropriateness of models that include only financial and economic measures to evaluate administrators when quality care is an expected output. The second issue is the appropriateness of using noncontrollable variables, in this case operating income, to evaluate administrators. We show how efficiency scores differ when quality variables and/or operating income are included. We also demonstrate the usefulness of DEA information to both the home administrator and chain managers for improving operating efficiency.     

A multistage method to measure efficiency and its application to Japanese banking industry

When measuring technical efficiency with existing data envelopment analysis (DEA) techniques, mean efficiency scores generally exhibit volatile patterns over time. This appears to be at odds with the general perception of learning-by-doing management, due to Arrow [The economic implications of learning by doing. Review of Economic Studies 1964; 154–73]. Further, this phenomenon is largely attributable to the fundamental assumption of deterministic data maintained in DEA models, and to the difficulty such models have in incorporating environmental influences. This paper proposes a three-stage method to measure DEA efficiency while controlling for the impacts of both statistical noise and environmental factors. Using panel data on Japanese banking over the period 1997–2001, we demonstrate that the proposed approach greatly mitigates these weaknesses of DEA models. We find a stable upward trend in mean measured efficiency, indicating that, on average, the bankers were learning over the sample period. Therefore, we conclude that this new method is a significant improvement relative to those DEA models currently used by researchers, corporate management, and industrial regulatory bodies to evaluate performance of their respective interests.     

Centralized Resource Allocation Using Data Envelopment Analysis

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.     

Integration of network data envelopment analysis and decision-making trial and evaluation laboratory for the performance evaluation of the financial holding companies in Taiwan

Data envelopment analysis (DEA) has been constantly used to measure the technical efficiency of decision-making units (DMUs). However, the major problem of traditional DEA methods is that they do not consider the possible intermediate effects. Recently, many papers have applied network DEA models to evaluate the efficiency scores. However, the linking activity of DMUs is still hard to be recognized. Hence, we employ DEMATEL to obtain the linking activity of DMUs. Our empirical research shows that the proposed method can soundly deal with the purpose of identifying the relationship between variables and derive the reasonable result in network DEA.     

Assessment and budget allocation of Iranian natural gas distribution company- A CSW DEA based model

Regarding the importance of budgeting in organizations, this research proposes an empirical approach to budget allocation problems. The methodological instrument utilized is data envelopment analysis (DEA) which is a nonparametric mathematical programming technique. In the DEA methodology a standard DEA model should be independently solved to evaluate each decision making unit (DMU). Consequently, it is hard to find the magnitude of budget for each DMU by applying a budget allocation model based on standard DEA models because identifying the DMU under evaluation is problematic. Also, to overcome problems of evaluation using standard DEA models, common set of weights (CSW) DEA models were suggested. These models can be developed for use in budget allocation DEA models that lead to finding a single magnitude of budget for each DMU. Moreover, the opinion of the decision maker can be incorporated into the model using budgetary constraints. As a result, a restricted linear budget allocation CSW DEA model is proposed in which the central authority would like to plan for improving the total efficiency scores of all DMUs. In essence, the proposed model is used to reallocate the available budget and, thus, the results obtained will be a suggestion for budget allocation in subsequent periods. Finally, the proposed model is applied to budget allocation in the Iranian gas industry in which the available budget is reallocated to increase the total efficiency scores of Iranian gas distribution branches.     

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

Qualitative data envelopment analysis by affinity set: a survey of subjective opinions for NPOs

Measuring the performance of Non-Profit Organizations (NPOs) is a complicated issue: data envelopment analysis (DEA) is a popular quantitative tool in the past literature. However, the subjective opinions of NPOs could disturb their actual performance, and this problem is seldom considered. In this study, we use the qualitative DEA as a tool to find the emphasized inputs and outputs for these NPOs. Most DEA models are established by the basis of quantitative data, they are difficult to describe the qualitative performance of NPOs. This paper proposes a new perspective for computing the efficiency of a Decision Making Unit based on qualitative data by affinity Set. The DEA model for qualitative data could be traced back to the work of Cook et al. early in 1993. Our contribution prevents the identical efficiency scores from the model of Cook et al., and a combinatorial optimization technique is used to solve the new problem. Finally, we found most NPOs would like to get more resources from outside; but interestingly, they don’t like to be officially monitored. Therefore, we should use the quantitative DEA on NPOs very carefully.     

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

Data envelopment analysis (DEA) is in fact more than just being an instrument for measuring the relative efficiencies of a group of decision making units (DMU). DEA models are also means of expressing appreciative democratic voices of DMUs. This paper proposes a methodology for allocating premium points to a group of professors using three models sequentially: (1) a DEA model for appreciative academic self-evaluation, (2) a DEA model for appreciative academic cross-evaluation, and (3) a Non-DEA model for academic rating of professors for the purpose of premium allocations. The premium results, called DEA results, are then compared with the premium points “nurtured” by the Dean, called N bonus points. After comparing DEA results and N bonus points, the Dean reassessed his initial bonus points and provided new ones – called DEA-N decisions. The experience indicates that judgmental decisions (Dean's evaluations) can be enhanced by making use of formal models (DEA and Non-DEA models). Moreover, the appreciative and democratic voices of professors are virtually embedded in the DEA models.     

关于DEA有效性理论的一点探索

给出经典的基于输入和输出的DEA模型,把基于DEA模型相结合的相对效率模型引入评价证券相对有效性,以风险作为输入,期望收益率作为输出,便可以用DEA模型评价每只证券相对有效性。     

Hierarchies and Groups in DEA

Conventional applications of data envelopment analysis (DEA) presume the existence of a set of similar decision making units, wherein each unit is evaluated relative to other members of the set. Often, however, the DMUs fall naturally into groupings, giving rise first to the problem of how to view the groups themselves as DMUs, and second to the issue of how to deal with several different ratings for any given DMU when groupings can be formed in different ways. In the present paper we introduce the concept of hierarchical DEA, where efficiency can be viewed at various levels. We provide a means for adjusting the ratings of DMUs at one level to account for the ratings received by the groups (into which these DMUs fall) at a higher level. We also develop models for aggregating different ratings for a DMU arising from different possible groupings. An application of these models to a set of power plants is given.     

Stochastic leader–follower DEA models for two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). In recent years, it has been widely used to evaluate two-stage systems under different organization mechanisms. This study modifies the conventional leader–follower DEA models for two-stage systems by considering the uncertainty of data. The dual deterministic linear models are first constructed from the stochastic CCR models under the assumption that all components of inputs, outputs, and intermediate products are related only with some basic stochastic factors, which follow continuous and symmetric distributions with nonnegative compact supports. The stochastic leader–follower DEA models are then developed for measuring the efficiencies of the two stages. The stochastic efficiency of the whole system can be uniquely decomposed into the product of the efficiencies of the two stages. Relationships between stochastic efficiencies from stochastic CCR and stochastic leader–follower DEA models are also discussed. An example of the commercial banks in China is considered using the proposed models under different risk levels.     

Using data envelopment analysis to measure the efficiency of non-profit organizations: A critical evaluation

This study examines the potential effects of variable set expansion and data variations upon the efficiency scores generated using the Data Envelopment Analysis (DEA) model. It was found that variable set expansion (either through disaggregation of existing variables or addition of new factors) should produce an upward trend in efficiency scores. In addition, ample opportunity exists for ‘decision-making units’ to increase their efficiency scores through manipulation of reported data. In real-world applications of DEA, these problems must be resolved as much as possible (e.g. increased audit of data) in order to improve DEA's practical usefulness and reliability.     

A novel method for computing single output for DEA with application in hospital efficiency

There are two main methods for measuring the efficiency of decision-making units (DMUs): data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Each of these methods has advantages and disadvantages. DEA is more popular in the literature due to its simplicity, as it does not require any pre-assumption and can be used for measuring the efficiency of DMUs with multiple inputs and multiple outputs, whereas SFA is a parametric approach that is applicable to multiple inputs and a single output. Since many applied studies feature multiple output variables, SFA cannot be used in such cases. In this research, a unique method to transform multiple outputs to a virtual single output is proposed. We are thus able to obtain efficiency scores from calculated virtual single output by the proposed method that are close (or even the same depending on targeted parameters at the expense of computation time and resources) to the efficiency scores obtained from multiple outputs of DEA. This will enable us to use SFA with a virtual single output. The proposed method is validated using a simulation study, and its usefulness is demonstrated with real application by using a hospital dataset from Turkey.     

The operating efficiency of financial holding and nonfinancial holding banks—Epsilou‐based measure metafrontier data envelopment analysis model

Previous bank efficiency studies assumed that the same efficient frontier system exists in different types of banks, but the conventional radial data envelopment analysis (DEA) model slacks are not counted in efficiency scores, and nonradial DEA models do not consider radial features. This paper develops an Epsilou‐based measure meta‐DEA approach for measuring the efficiencies and technology gaps of different bank types. The results are as the follows: The average efficiency and technology gaps of nonfinancial holding banks are better than those of financial holding banks. The nonfinancial holding banks are more efficient than financial holding banks in investment and other income.     

DEA模型评价第三方物流企业服务项目绩效的应用分析

以物流成本投入与收益为输入和输出指标,通过运用DEA模型对我国某第三方物流企业的7个物流服务项目进行综合绩效评价与分析。找出企业在物流项目运作中的问题,对非DEA有效的投入和产出给出调整意见加以改进。     

Lower Bound Restrictions on Intensities in Data Envelopment Analysis

We propose an extension to the basic DEA models that guarantees that if an intensity is positive then it must be at least as large as a pre-defined lower bound. This requirement adds an integer programming constraint known within Operations Research as a Fixed-Charge (FC) type of constraint. Accordingly, we term the new model DEA_FC. The proposed model lies between the DEA models that allow units to be scaled arbitrarily low, and the Free Disposal Hull model that allows no scaling. We analyze 18 datasets from the literature to demonstrate that sufficiently low intensities—those for which the scaled Decision-Making Unit (DMU) has inputs and outputs that lie below the minimum values observed—are pervasive, and that the new model ensures fairer comparisons without sacrificing the required discriminating power. We explain why the low-intensity phenomenon exists. In sharp contrast to standard DEA models we demonstrate via examples that an inefficient DMU may play a pivotal role in determining the technology. We also propose a goal programming model that determines how deviations from the lower bounds affect efficiency, which we term the trade-off between the deviation gap and the efficiency gap.     

Productivity drivers and market dynamics in the Spanish first division football league

This paper analyses efficiency drivers of a representative sample of Spanish football clubs by means of the two-stage data envelopment analysis (DEA) procedure proposed by Simar and Wilson (J Econ, 136:31–64, 2007). In the first stage, the technical efficiency of football clubs is estimated using a bootstrapped DEA model in order to establish which of them are the most efficient; the ranking is based on total productivity in the period 1996–2004. In the second stage, the Simar and Wilson (J Econ, 136:31–64, 2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. Policy implications of the main findings are also considered.     

Two-stage DEA: <Emphasis Type="Italic">caveat emptor</Emphasis>

This paper examines the wide-spread practice where data envelopment analysis (DEA) efficiency estimates are regressed on some environmental variables in a second-stage analysis. In the literature, only two statistical models have been proposed in which second-stage regressions are well-defined and meaningful. In the model considered by Simar and Wilson (J Prod Anal 13:49–78, 2007), truncated regression provides consistent estimation in the second stage, where as in the model proposed by Banker and Natarajan (Oper Res 56: 48–58, 2008a), ordinary least squares (OLS) provides consistent estimation. This paper examines, compares, and contrasts the very different assumptions underlying these two models, and makes clear that second-stage OLS estimation is consistent only under very peculiar and unusual assumptions on the data-generating process that limit its applicability. In addition, we show that in either case, bootstrap methods provide the only feasible means for inference in the second stage. We also comment on ad hoc specifications of second-stage regression equations that ignore the part of the data-generating process that yields data used to obtain the initial DEA estimates.     

Learning from input–output mixes in DEA: a proportional measure for slack‐based efficient projections

Several Data Envelopment Analysis (DEA) models use a radial distance measure that is based on the Debreu–Farrell notion of (in)efficiency. While this measure has an attractive interpretation, its use may be problematic if slacks or zeros are present in the data. The additive DEA model can perfectly deal with these problems, but the meaning of its associated scores is less intuitive than the one attached to the radial measures. We introduce an alternative efficiency measure, based on the results of the additive model, that can be decomposed in a Debreu–Farrell component and a factor that captures differences in input–output mixes with respect to those of the best practice reference observation. On an aggregate level, this second component can be considered as an indicator of the dispersion between radial efficiency measurement and results based on the Pareto–Koopmans efficiency notion. On the individual level, the measure allows us to regard relative inefficiency as resulting from (i) a divergence of implicit cost price vectors, and (ii) a cost level that is too high, even after adjustment for the implicit cost prices. Copyright © 1999 John Wiley & Sons, Ltd.     

基于L-R型模糊DEA的模型改进

本文首先介绍了前人建立的模糊DEA模型,考虑这些模型存在人为提高效率值、未充分利用模糊信息、计算量过大的问题,建立了一个新的L-R DEA模型,该模型基于α-截集的模糊数变换,将指标集分解为多个指标子集,分别对每个子集进行效率计算,最后应用熵值法确定决策单元(DMU)的最终效率值。该方法可以对DMU进行充分排序,扩大了DEA的应用领域。文末通过一算例来说明新模型的有效性。