Scaling units via the canonical correlation analysis in the DEA context

This paper deals with the evaluation of decision making units which have multiple inputs and outputs. A new method (CCA/DEA) is developed where the Canonical Correlation Analysis (CCA) is utilized to provide a full rank scaling for all the units rather than a categorical classification (for efficient and inefficient units) as done by the Data Envelopment Analysis (DEA). The CCA/DEA approach is an attempt to bridge the gap between the frontier approach of DEA and the average tendencies of statistics (econometrics). Nonparametric statistical tests are employed to validate the consistency between the classification from the DEA and the postclassification that was generated by the CCA/DEA.     

Strategic groups based on marginal rates: An application to the Spanish banking industry

This paper uses Data Envelopment Analysis (DEA) to identify strategic groups (SGs) in the Spanish banking industry. The concept of SG relies on the fact that firms grouped together value inputs and outputs in the same way. As such, they take identical direction when, due to external influences, changes are required. Weights obtained from DEA are extremely useful in the valuation of inputs and outputs. Specifically, by comparing DEA weights pair-wise, i.e. quantifying the variables’ marginal rates (MR), we can obtain a very good representation of the existent trade-off and the relative importance of the two variables.The paper uses MRs obtained through DEA models and, simultaneously, proposes feasible ways to overcome two usual problems with DEA virtual weights, namely: (1) the multiplicity of weights for efficient DMUs; and (2) the inexistence of dual variables for inefficient DMUs.From the empirical point of view, once the MRs are determined, the second stage is to perform Cluster Analysis. We apply Cluster Analysis in two ways: (1) on the basis of the MRs; and (2) following the traditional application by running Cluster Analysis with the original variables. The results obtained show the advantages of using MRs instead of the standard application of Cluster Analysis.Summing up, the concept of SG is reinforced if we use refined methods to determine the existence of SGs. The results of the application of DEA models to observe the presence of SG in the Spanish banking industry offer interesting views on it.     

Sensitivity and stability in stochastic data envelopment analysis

Sensitivity and stability for Banker's model of Stochastic Data Envelopment Analysis (SDEA) is studied in this paper. In the case of the DEA model, necessary and sufficient conditions to preserve the efficiency of efficient decision-making units (DMUs) and the inefficiency of inefficient DMUs are obtained for different perturbations of data in the model. The cases of perturbations of all inputs, of perturbations of output and of the simultaneous perturbations of output and all inputs are considered. An illustrative example is provided.     

Chapter 12 New uses of DEA and statistical regressions for efficiency evaluation and estimation — with an illustrative application to public secondary schools in Texas

This paper examines new combinations of Data Envelopment Analysis (DEA) and statistical approaches that can be used to evaluate efficiency within a multiple-input multiple-output framework. Using data on five outputs and eight inputs for 638 public secondary schools in Texas, unsatisfactory results are obtained initially from both Ordinary Least Squares (OLS) and Stochastic Frontier (SF) regressions run separately using one output variable at-a-time. Canonical correlation analysis is then used to aggregate the multiple outputs into a single aggregate output, after which separate regressions are estimated for the subsets of schools identified as efficient and inefficient by DEA. Satisfactory results are finally obtained by a joint use of DEA and statistical regressions in the following manner. DEA is first used to identify the subset of DEA-efficient schools. The entire collection of schools is then comprehended in a single regression with dummy variables used to distinguish between DEA-efficient and DEA-inefficient schools. The input coefficients are positive for the efficient schools and negative and statistically significant for the inefficient schools. These results are consistent with what might be expected from economic theory and are informative for educational policy uses. They also extend the treatments of production functions usually found in the econometrics literature to obtain one regression relation that can be used to evaluate both efficient and inefficient behavior.     

Invariant multiplicative efficiency and piecewise cobb-douglas envelopments

A new multiplicative efficiency formulation is developed wherein the efficiency values are invariant under changes in the units of measurement of outputs and inputs. It is shown that the associated Data Envelopment Analysis (DEA) implies that optimal envelopments are of piecewise Cobb-Douglas type. This leads to a new method for estimating frontier production functions of Cobb-Douglas type.     

A generalized DEA model for inputs/outputs estimation

In this paper we discuss the question: among a group of decision making units (DMUs), if a DMU changes some of its input (output) levels, to what extent should the unit change outputs (inputs) such that its efficiency index remains unchanged? In order to solve this question we propose a solving method based on Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP). In our suggested method, the increase of some inputs (outputs) and the decrease due to some of the other inputs (outputs) are taken into account at the same time, while the other offered methods do not consider the increase and the decrease of the various inputs (outputs) simultaneously. Furthermore, existing models employ a MOLP for the inefficient DMUs and a linear programming for weakly efficient DMUs, while we propose a MOLP which estimates input/output levels, regardless of the efficiency or inefficiency of the DMU. On the other hand, we show that the current models may fail in a special case, whereas our model overcomes this flaw. Our method is immediately applicable to solve practical problems.     

Super-efficiency in DEA by effectiveness of each unit in society

One of the most important topics in management science is determining the efficiency of Decision Making Units (DMUs). The Data Envelopment Analysis (DEA) technique is employed for this purpose. In many DEA models, the best performance of a DMU is indicated by an efficiency score of one. There is often more than one DMU with this efficiency score. To rank and compare efficient units, many methods have been introduced under the name of super-efficiency methods. Among these methods, one can mention Andersen and Petersen’s (1993) [1] super-efficiency model, and the slack-based measure introduced by Tone (2002) [4]. Each of the methods proposed for ranking efficient DMUs has its own advantages and shortcomings. In this paper, we present a super-efficiency method by which units that are more effective and useful in society have better ranks. In fact, in order to determine super-efficiency by this method, the effectiveness of each unit in society is considered rather than the cross-comparison of the units. To do so, we divide the inputs and outputs into two groups, desirable and undesirable, at the discretion of the manager, and assign weights to each input and output. Then we determine the rank of each DMU according to the weights and the desirability of inputs and outputs.     

Centralized resource allocation with stochastic data

Data Envelopment Analysis (DEA) is a technique based on mathematical programming for evaluating the efficiency of homogeneous Decision Making Units (DMUs). In this technique inefficient DMUs are projected on to the frontier which constructed by the best performers. Centralized Resource Allocation (CRA) is a method in which all DMUs are projected on to the efficient frontier through solving just one DEA model. The intent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA) in order to allocate centralized resources where inputs and outputs are stochastic. The concept discussed throughout this paper is illustrated using the aforementioned example.     

Common set of weights in data envelopment analysis: a linear programming problem

Data Envelopment Analysis is used to determine the relative efficiency of Decision Making Units as the ratio of weighted sum of outputs by weighted sum of inputs. To accomplish the purpose, a DEA model calculates the weights of inputs and outputs of each DMU individually so that the highest efficiency can be estimated. Thus, the present study suggests an innovative method using a common set of weights leading to solving a linear programming problem. The method determines the efficiency score of all DMUs and rank them too.     

Cross-efficiency evaluation with directional distance functions

This paper extends the cross-efficiency evaluation for use with directional distance functions. Cross-efficiency evaluation has been developed with oriented Data Envelopment Analysis (DEA) models, so the extension proposed here is aimed at providing a peer-evaluation of decision making units (DMUs) based on measures that account for the inefficiency both in inputs and in outputs simultaneously. We explore the duality relations regarding the models of directional distance functions and define the cross-efficiencies on the basis of the equivalences with some fractional programming problems. Finally, we address in this new context the problem with the alternate optima for the weights and propose some models that implement different alternative secondary goals.     

Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

Studies of some duality properties in the Li and Reeves model

In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.     

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.     

DEA models with undesirable inputs and outputs

Data Envelopment Analysis (DEA) models with undesirable inputs and outputs have been frequently discussed in DEA literature, e.g., via data transformation. These studies were scatted in the literature, and often confined to some particular applications. In this paper we present a systematic investigation on model building of DEA without transferring undesirable data. We first describe the disposability assumptions and a number of different performance measures in the presence of undesirable inputs and outputs, and then discuss different combinations of the disposability assumptions and the metrics. This approach leads to a unified presentation of several classes of DEA models with undesirable inputs and/or outputs.     

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.     

Finding strong defining hyperplanes of Production Possibility Set

Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. Data Envelopment Analysis models implicitly use PPS to evaluate relative efficiency of Decision Making Units (DMUs). Although DEA models can determine the efficiency of a DMU, they cannot present efficient frontiers of PPS. In this paper, we propose a method for finding all Strong Defining Hyperplanes of PPS (SDHP). They are equations that form efficient surfaces. These equations are useful in Sensitivity and Stability Analysis, the status of Returns to Scale of a DMU, incorporating performance information into the efficient frontier analysis and so on.     

Radii of Classification Preservation in Data Envelopment Analysis: a Case Study of ‘Program Follow-Through’

Sensitivity and robustness of efficiency classifications for the additive model and its geometric equivalents in Data Envelopment Analysis (DEA) are addressed. The minimum distance (measured by a Tchebycheff norm) separating an organization from reclassification is computed via linear programming formulations and shown to constitute a generalized ‘residual’ for each organization. Without this sensitivity information, findings can be distorted when marginally efficient or inefficient units are distinguished solely on the basis of their classification. Analysis of these residuals from an earlier (inconclusive) DEA study further reveals how substantive differences in a sample's underlying groups can be detected. Properties of group efficiency and group proximity to the efficient frontier are investigated using these new indicators.     

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.     

Measuring production with random inputs and outputs using DEA and certainty equivalent

This study evaluates production operations with inputs/outputs under random influences. We introduce a measurement of efficiency using utility function families. Applying Data Envelopment Analysis (DEA) and the certainty equivalent, the proposed measurement is capable of accommodating various risk attitudes of evaluators.