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

Ranking intervals for two-stage production systems

Traditional Data Envelopment Analysis (DEA) models find the most desirable weights for each Decision Making Unit (DMU) in order to estimate the highest efficiency score as possible. Usually, decision-makers are using these efficiency scores for ranking the DMUs. The main drawback in this process is that the ranking based on weights obtained from the standard DEA models ignore other feasible weights, this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black box” and developed a mix-integer model to obtain the ranking intervals for each DMU over sets of all its feasible weights. In many real-world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka (2011)’s model to more common and practical applications considering the two-stage production structure. The proposed approach calculates each DMU’s ranking interval for the overall system as well as for each subsystem/sub-stage. An application for non-life insurance companies is given to illustrate the applicability of the proposed approach. A real application in Chinese commercial banks shows how this approach can be used by policy makers

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

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

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 – 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

A Fuzzy Data Envelopment Analysis Framework for Dealing with Uncertainty Impacts of Input–Output Life Cycle Assessment Models on Eco-efficiency Assessment

The uncertainty in the results of input–output-based life cycle assessment models makes the sustainability performance assessment and ranking a challenging task. Therefore, introducing a new approach, fuzzy data envelopment analysis, is critical; since such a method could make it possible to integrate the uncertainty in the results of the life cycle assessment models into the decision-making for sustainability benchmarking and ranking. In this paper, a fuzzy data envelopment analysis model was coupled with an input–output-based life cycle assessment approach to perform the sustainability performance assessment of the 33 food manufacturing sectors in the United States. Seven environmental impact categories were considered the inputs and the total production amounts were identified as the output category, where each food manufacturing sector was considered a decision-making unit. To apply the proposed approach, the life cycle assessment results were formulated as fuzzy crisp valued-intervals and integrated with fuzzy data envelopment analysis model, thus, sustainability performance indices were quantified. Results indicated that majority (31 out of 33) of the food manufacturing sectors were not found to be efficient, where the overall sustainability performance scores ranged between 0.21 and 1.00 (efficient), and the average sustainability performance was found to be 0.66. To validate the current study\u27s findings, a comparative analysis with the results of a previous work was also performed. The major contribution of the proposed framework is that the effects of uncertainty associated with input–output-based life cycle assessment approaches can be successfully tackled with the proposed Fuzzy DEA framework which can have a great area of application in research and business organizations that use with eco-efficiency as a sustainability performance metric

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

Multiregional sustainability at a sectoral level: Towards more effective environmental regulations

Aquesta tesi està dedicada al desenvolupament d'eines per ajudar als responsables polítics en la creació de normatives eficaces de manera eficient i metòdica. La tesi està organitzada en quatre seccions principals. A la secció 1, presentem la introducció, on establim les bases dels mètodes i dades utilitzades en aquest treball, així com els buits bibliogràfics que cobrim amb els nostres estudis. La secció 2 es basa en el primer treball, on estudiem l'eco-eficiència dels sectors manufacturers de la UE combinant taules MREEIO amb el mètode DEA i seguint aproximacions basades en la producció i el consum. Això permet identificar els sectors que requereixen regulacions en impactes específics. A continuació, a la secció 3, utilitzem DEA per determinar l'eficiència de sostenibilitat dels mixos elèctrics de la UE analitzant els trets socials, econòmics i ambientals de cadascun d’ells. En una segona etapa, utilitzem un model matemàtic a mida anomenat EffMixF per obtenir la nova composició elèctrica per als països que han resultat ineficients en la primera etapa. Aquests nous mixos es poden utilitzar com a full de ruta en l’elaboració de normatives específiques per al sector, indicant quines tecnologies s'han de fomentar, o bé obstaculitzar a cada país ineficient. Finalment, a la secció 4, determinem els factors clau de l'impacte ambiental a escala global. Per aconseguir-ho, primer comparem dues tècniques de descomposició, els mètodes SDA i Shapley-Sun, per tal d’establir les seves similituds i introduir una equació general simplificada que es pot utilitzar en substitució d’ambdós mètodes. Per acabar, apliquem aquests mètodes en un cas d’estudi, on considerem una selecció d’impactes ambientals en un període de 15 anys, per determinar la utilitat dels mètodes de descomposició. Les eines desenvolupades en aquesta tesis proporcionen informació valuosa respecte a les debilitats i oportunitats de millora dels sectors econòmics a nivell macroeconòmic.Esta tesis está dedicada al desarrollo de herramientas para ayudar a los responsables políticos en la creación de regulaciones efectivas de manera eficiente y metódica. La tesis contiene cuatro secciones principales. En la sección 1, presentamos la introducción, donde se establecen los métodos y datos utilizados en esta tesis, así como las lagunas bibliográficas que cubrimos con nuestros estudios. La sección 2 se basa en el primer trabajo, donde estudiamos la ecoeficiencia de los sectores manufactureros de la UE mediante la combinación de las tablas MREEIO con el método DEA y siguiendo enfoques basados en la producción y el consumo. Esto nos permite identificar los sectores que requieren regulaciones en impactos específicos. A continuación, en la sección 3 usamos DEA para determinar la eficiencia de sostenibilidad de los mixes eléctricos de la UE analizando las características sociales, económicas y medioambientales de cada uno de ellos. En una segunda etapa, utilizamos un modelo matemático a medida llamado EffMixF para obtener nuevos mixes eléctricos para los países ineficientes. Estos nuevos mixes pueden ser utilizados como plan estrategico en la elaboración de reglamentos específicos para el sector, indicando qué tecnologías deben ser fomentadas, o bien obstaculizadas, en cada país ineficiente. Finalmente, en la sección 4, determinamos los factores clave del impacto ambiental a escala global. Para conseguirlo, primero comparamos dos técnicas de descomposición, SDA y Shapley-Sun, para establecer sus similitudes e introducir una ecuación general simplificada como sustitución de ambos métodos. Posteriormente, aplicamos estos métodos en un caso de estudio donde consideramos una selección de impactos ambientales en un período de 15 años para determinar la utilidad de los métodos de descomposición. Las herramientas desarrolladas en esta tesis proporcionan información valiosa respecto a las debilidades y oportunidades de los sectores económicos a nivel macroeconómico.This thesis is dedicated to the development of tools to assist policy makers in the creation of effective regulations in an efficient and methodical way. The thesis is organized into four main sections. In section 1, we present the introduction, where we establish the background of the methods and data used in this work, as well as the literature gaps that we cover with our studies. Section 2 is based on the first work, where we study the eco-efficiency of the EU manufacturing sectors by combining MREEIO tables with the DEA method, following the production and consumption-based approaches. This allows us to identify the sectors requiring regulations in specific burdens. Then, in section 3, we use DEA to determine the sustainability efficiency of the EU electricity mixes by analyzing the social, economic and environmental features of each portfolio. In a second stage, we use a tailored mathematical model named EffMixF to obtain new electricity mixes for the countries found inefficient in the previous step. These new mixes can be used as roadmap to devise specific regulations for the sector, indicating which technologies should be boosted and which hindered in each inefficient country. Finally, in section 4, we determine the key driving factors of the environmental impact on a global scale. For this, we first compare two decomposition techniques, the SDA and the Shapley-Sun methods, establishing their similarities and introducing a simplified general equation that can be used in substitution of both methods. Then, we apply these methods in a case study, where we consider a selection of environmental impacts in a 15-year period, to determine the usefulness of the decomposition methods. The tools developed in this thesis provide valuable insight regarding the weaknesses and improvement opportunities of the economic sectors in a macroeconomic scale

Efficiency analysis of information technology and online social networks management : an integrated DEA-Model assessment

This paper analyses the relationship between productive efficiency and online-social-networks (OSN) in Spanish telecommunications firms. A data-envelopment-analysis (DEA) is used and several indicators of business ?social Media? activities are incorporated. A super-efficiency analysis and bootstrapping techniques are performed to increase the model?s robustness and accuracy. Then, a logistic regression model is applied to characterise factors and drivers of good performance in OSN. Results reveal the company?s ability to absorb and utilise OSNs as a key factor in improving the productive efficiency. This paper presents a model for assessing the strategic performance of the presence and activity in OSN