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.     

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.     

Equivalences between Data Envelopment Analysis and the theory of redundancy in linear systems

This paper establishes how the non-parametric frontier estimation methodology of Data Envelopment Analysis (DEA) and the classical problem of detecting redundancy in a system of linear inequalities are connected. We present an analysis of the sets generated in two of DEA's models from where the empirical efficient production frontier is established from the point of view of polyhedral set theory. This yields convenient alternative characterizations of these sets which provide new insights about their properties. We use these insights to show how these polyhedral sets connect DEA to redundancy in linear systems. This means that DEA can benefit from a rich and well-established collection of computational and theoretical results which apply directly from redundancy in linear systems.     

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.     

The Adjusted Spherical Frontier Model with weight restrictions

This paper presents the ASFM-lp model, a parametric Data Envelopment Analysis (DEA) model for allocating resources, commonly called inputs. This model considers that a fair allocation of inputs is one that maximizes the DEA-CCR efficiencies of the Decision Making Units (DMUs). The main assumption of the ASFM-lp is the predefined spherical shape of the efficiency frontier. We have demonstrated that our method extends the existing parametric model ASFM to allow the introduction of weight restrictions, which has great importance in practical applications of DEA. Numeric examples are presented to show the application of the method.     

The relevance of DEA benchmarking information and the Least-Distance Measure

Efficiency analysis is performed not only to estimate the current level of efficiency, but also to provide information on how to remove inefficiency, that is, to obtain benchmarking information. Data Envelopment Analysis (DEA) was developed in order to satisfy both objectives and the strength of its benchmarking analysis gives DEA a unique advantage over other methodologies of efficiency analysis. This study proposes the use of the Least-Distance Measure in order to obtain the shortest projection from the evaluated Decision Making Unit (DMU) to the strongly efficient production frontier, thus allowing an inefficient DMU to find the easiest way to improve its efficiency. In addition to producing reasonable benchmarking information, the proposed model provides efficiency values which satisfy the general requirements that every well-defined efficiency measure should meet.     

Spherical frontier DEA model based on a constant sum of inputs

In this paper, a Data Envelopment Analysis (DEA) model in which a fixed input needs to be assigned to a group of Decision-Making Units (DMUs) is presented. This is performed by assuming the existence of a geometric place represented by a sphere that characterizes the DEA frontier. It is shown that, under this assumption, it becomes relatively easy to find a way to distribute the fixed input to all DMUs, by considering that the individual assignments will be fair through the requirement that all DMUs be efficient or, in other words, be located on the spherically shaped efficiency frontier. A model is presented and results are compared to those obtained by using two different methods proposed in the literature within the same context.     

Determining a sequence of targets in DEA

Data Envelopment Analysis (DEA) can be used for assessing the relative efficiency of a number of operating units, finding, for each inefficient unit, a target operating point lying on the efficient frontier. Most DEA models project an inefficient unit onto a most distant target, which makes its attainment more difficult. In this paper, we advocate determining a sequence of targets, each one within an appropriate, short distance of the preceding. The proposed Constant Returns to Scale approach has two interesting features: (a) the sequence of targets ends in the efficient frontier and (b) the final, efficient target is generally closer to the original unit than the one-step projection is.     

Identification of Pareto-efficient facets in data envelopment analysis

In Data Envelopment Analysis (DEA), identification of the Pareto-efficient frontier of an empirical production possibility set is a prerequisite step toward determining rates of change of outputs with changes in inputs along its piecewise linear facets. These rates of change, which will be different on different facets, have important economic and managerial implications in trade-off analysis, forecasting and resource allocation. Accurate and complete identification of the component members of each facet remains an open question. Such identification is important in certain procedures for determining these rates of change. This paper develops three modifications to the pivoiing criteria of the simplex algorithm, commonly used to solve DEA problems, as alternative strategies for more completely identifying facet members of the Pareto-optimal frontier common to several production possibility sets in DEA. Experimental results from implementing these strategies are presented.     

Estimation of potential gains from mergers in multiple periods: a comparison of stochastic frontier analysis and Data Envelopment Analysis

A new dynamic Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the merger performance. This new approach allows us to dynamically evaluate the pre-merger firms and the post-merger firm in a multi-period situation. A case study of bank branch merger is conducted to illustrate and validate the proposed approach. Both stochastic frontier analysis and data envelopment analysis are used and compared leading to highly correlated results. The computation show that merger results in an overall efficiency achievement in a banking industry.     

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.     

Negative data in DEA: a simple proportional distance function approach

The need to adapt Data Envelopment Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. A recent article in this journal proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accommodate the occurrence of negative data. In this contribution, we define and recommend a generalised Farrell proportional distance function that can do the same job and that maintains a proportional interpretation under mild conditions.     

Improving the discriminating power of DEA: focus on globally efficient units

We introduce in this paper the global efficiency approach as a means to improve the discriminating power of Data Envelopment Analysis (DEA). To discriminate further among the DEA efficient units, we deal only with the units that can maintain their efficiency score under common weighting structures. Then we proceed further to ranking the whole set of DEA efficient units. We compare the global efficiency approach with the multi-criteria DEA and the cross-efficiency approaches on the basis of characteristic numerical examples drawn from the literature.     

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.     

Short-run and long-run efficiency measures for multiplant firms

The usual Data Envelopment Analysis (DEA) model for measuring the relative efficiency assumes that all plants belong to distinct firms superior to them. For firms with more than one plant, Koopmans proposes a procedure for deriving the short-run production frontier for each firm. Modifying his idea, a DEA model is constructed in this paper for measuring the short-run efficiency of each plant within a firm. Based on the theory of production economics that the long-run production frontier is an envelop super-imposed upon all short-run production frontiers, another DEA model is constructed to measure the long-run efficiency of every plant. The long-run efficiency is always smaller than or equal to the short-run efficiency. Consequently, it is possible that an inefficient plant can only be improved in the long-run. With the models constructed in this paper, a decision-maker is able to distinguish between what can be achieved in the short-run and what in the long-run. To clarify the idea, an example of Taiwan forests is adopted for illustration. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measuring the joint impact of governance form and economic regulation on airport efficiency

This paper examines the joint impact that governance structure and economic regulation has on airport efficiency. The previous literature has focused on one or the other of these factors but not both. The empirical investigation uses a semi-parametric Bayesian distance stochastic frontier model, as well as a Data Envelopment Analysis (DEA) model. Based on a panel of airports in several countries we find that the form of economic regulation is relatively more important than the type of governance in affecting efficiency. The article provides measures of changes in expected efficiency when either or both the governance form and price regulation changes.     

基于DEA的出版社相对有效性评价

利用数据包络分析方法(简称DEA方法)对几个教育类出版社的职工人数结构与定价总额之间关系进行了分析,发现有些出版社是DEA有效的,而有些则不是.对非DEA有效的出版社来说,可以通过调整投入以获得同样产出,从而提高经济效益.     

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.     

The overall efficiency of the dynamic DEA models

Central European Journal of Operations Research - This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA...