New tools for dealing with errors-in-variables in DEA.

Errors in variables; Tool;

New Tools for Dealing with Errors-in-Variables in DEA.

We develop a series of novel conceptual tools to systematically account for errors-in-variables in Data Envelopment Analysis (DEA). These tools allow for statistical inference while requiring minimal statistical distribution assumptions, and therefore constitute a valuable addition to the tools currently available for dealing with errors-in-variables. An empirical application for large European Union financial institutions illustrates the proposed approach.Data Envelopment Analysis (DEA), errors-in-variables, efficiency depth, robust reference sets, financial institutions

Robust DEA efficiency scores: A probabilistic/combinatorial approach

In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This proba- bilistic approach allows us to obtain three different robust efficiency scores: the Conditional Expected Score, the Unconditional Expected Score and the Expected score under the assumption of Maximum Entropy principle. The calculation of the three efficiency scores involves the resolution of an exponential number of linear problems. The algorithm presented in this paper allows to solve over 200 millions of linear problems in an affordable time when considering up 20 inputs/outputs and 200 DMUs. The approach proposed is illustrated with an application to the assessment of professional tennis players

Multi-Criteria versus Data Envelopment Analysis for Assessing the Performance of Biogas Plants

This paper compares multi-criteria decision aiding (MCDA) and data envelopment analysis (DEA) approaches for assessing renewable energy plants, in order to determine their performance in terms of economic, environmental, and social criteria and indicators. The case is for a dataset of 41 agricultural biogas plants in Austria using anaerobic digestion. The results indicate that MCDA constitutes an insightful approach, to be used alternatively or in a complementary way to DEA, namely in situations requiring a meaningful expression of managerial preferences regarding the relative importance of evaluation aspects to be considered in performance assessment.Multi-criteria decision analysis; DEA; Renewable energy; Biogas

Super-efficiency and stability intervals in additive DEA

This is a PDF file of an unedited manuscript that has been accepted for publication in Journal of the Operational Research Society. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. The final version will be available at: http://dx.doi.org/10.1057/jors.2012.1

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input \u2013 output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Robustness analysis based on weight restrictions in data envelopment analysis

Includes bibliographical references.Evaluating the performance of organisations is essential to good planning and control. Part of this process is monitoring the performance of organisations against their goals. The comparative efficiency of organizations using common inputs and outputs makes it possible for organizations to improve their performance so that can operate as the most efficient organizations. Resources and outputs can be very diversified in nature and it is complex to assess organizations using such resources and outputs. Data Envelopment Analysis models are designed to facilitate this of assessment and aim to evaluate the relative efficiency of organisations. Chapter 2 is dedicated to the basic Data Envelopment Analysis. We present the following: * A review of the Data Envelopment Analysis models; * The properties and particularities of each model. In chapter 3, we present our literature survey on restrictions. Data Envelopment Analysis is a value-free frontier which has the of yielding more objective efficiency measures. However, the complete freedom in the determination of weights for the factors and products) relevant to the assessment of organisations has led to some problems such as: zero-weights and lack of discrimination between efficient organizations. Weight restriction methods were introduced in order to tackle these problems. The first part of chapter 3 in detail the motivations for weight restrictions while the second part presents the actual weight restriction rnethods

Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry

AbstractThis paper extends the conventional DEA models to a robust DEA (RDEA) framework by proposing new models for evaluating the efficiency of a set of homogeneous decision-making units (DMUs) under ellipsoidal uncertainty sets. Four main contributions are made: (1) we propose new RDEA models based on two uncertainty sets: an ellipsoidal set that models unbounded and correlated uncertainties and an interval-based ellipsoidal uncertainty set that models bounded and correlated uncertainties, and study the relationship between the RDEA models of these two sets, (2) we provide a robust classification scheme where DMUs can be classified into fully robust efficient, partially robust efficient and robust inefficient, (3) the proposed models are extended to the additive DEA model and its efficacy is analyzed with two imprecise additive DEA models in the literature, and finally, (4) we apply the proposed models to study the performance of banks in the Italian banking industry. We show that few banks which were resilient in their performance can be robustly classified as partially efficient or fully efficient in an uncertain environment