Implementing DEA models in the R program

Data Envelopment Analysis with R

Using data envelopment analysis as a mathematical performance evaluation tool is much more serious for researchers and practitioners. Different data envelopment analysis models are now introduced in different fields. In addition to the classic performance evaluation models in data envelopment analysis, developed models such as super-efficiency, returns to scale, progress and regress models, and so on have been introduced in this technique that help different aspects of analytics and decision making units in performance evaluation. In this chapter, such developed DEA models are formulated, and then the corresponding R codes for these models are provided.

European Journal of Operational Research, 2006

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GRIPS Discussion Papers, 2007

Liberalization of the electric power industry has been underway in various countries.

This paper aims to present an implementation of the DEA cross-efficiency models in the environment R. R is a free software and open source, highly extensible that offers a variety of functions and graphical routines for data analysis. We develop R codes for both formulations aggressive and benevolent of the DEA cross-efficiency models. In order to illustrate a practical application of the R codes we use inputs and outputs from Brazilian electricity distribution utilities.

Advances in DEA Theory and Applications, 2017

Data envelopment analysis (DEA) models started from the seminal paper by Charnes, Cooper and Rhodes [1] (hereafter referred to as CCR). This opened up fertile territory for efficiency evaluation. This paper has been cited by more than 20 000 papers as of the publication date of this book. CCR extended Farrell's work [2] to models with multiple inputs and multiple outputs by utilizing linear programming technology and succeeded in establishing DEA as a powerful basis for efficiency analysis. 1.2 BASIC DATA DEA compares the relative efficiency of a set of enterprises, called DMUs (decisionmaking units), which have common input and output factors. Let the numbers of DMUs, inputs and outputs be n, m and s, respectively. We denote input i and output r of DMU j by x ij i = 1,…, m; j = 1,…, n and y rj r = 1,…, s; j = 1,…, n , respectively. The input and output vectors for DMU h (h = 1,…,n) are defined as x h = x 1h ,…, x mh T and y h = y 1h ,…,y sh T. The input and output matrices are defined 0003038388.3D 3 25/3/2017 2:30:30 PM Advances in DEA Theory and Applications: With Extensions to Forecasting Models, First Edition. Edited by Kaoru Tone.

Pesquisa Operacional, 2002

Doklady Mathematics, 2016

Some inadequate results may appear in the DEA models as in any other mathematical model. In the DEA scientific literature several methods were proposed to deal with these difficulties. In our previous paper, we introduced the notion of terminal units. It was also substantiated that only terminal units form necessary and sufficient sets of units for smoothing the frontier. Moreover, some relationships were established between terminal units and other sets of units that were proposed for improving the frontier. In this paper we develop a general algorithm for improving the frontier. The construction of algorithm is based on the notion of terminal units. Our theoretical results are verified by computational results using real-life data sets and also confirmed by graphical examples.

When solving Data Envelopment Analysis (DEA) models it is usual to solve a Linear Programme (LP) many times, with different right-hand-side (RHS) vectors: once for each Decision Making Unit (DMU) in the organisation being evaluated. Besides being tedious and involving repeated computation this iterative approach gives little insight into the overall structure of the model for the organisation. Instead, by projecting out all the variables of the LP which are common to all LP runs, we obtain a formula into which we can substitute the inputs and outputs of each DMU in turn in order to obtain its efficiency number and efficient comparators. In addition we also obtain the best weightings which the DMU would choose to put on its inputs and outputs. The method of projection, which we use, is Fourier-Motzkin Elimination. This provides us with a finite number of extreme rays of the elimination cone. These rays give the dual multipliers which can be interpreted as weights which will apply to the inputs and outputs for particular DMUs. As the approach provides all the extreme rays of the cone, multiple sets of weights, when they exist, are explicitly provided. The method also demonstrates that the same weightings will apply to all DMUs having the same comparators. In addition it is possible to construct the skeleton of the efficient frontier of efficient DMUs.

2010

We describe an application of Data Envelopment Analysis (DEA) to evaluate the "X-factor" of a pricing model, which was created for the agency that regulates the privatised electricity distribution industry in Brazil. Both theoretical and client-led practical considerations in developing the final (1-input,4-output) DEA model are described. The usual economic interpretation of similar models developed in the literature that covers the electricity and water distribution industries has been enhanced through a simple diagrammatic representation of the results in 2-d. Finally, a critical evaluation of the VRS model of DEA has led to dynamic clustering as a more satisfactory alternative for comparing units of varying size.

Journal of the Operational Research Society, 2009

Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show 'a notoriously inefficient unit' as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.