Data envelopment analysis (DEA) is a relative technical efficiency measurement tool, which uses operations research techniques to automatically calculate the weights assigned to the inputs and outputs of the production units being assessed. The actual input/output data values are then multiplied with the calculated weights to determine the efficiency scores. Recent variants of the DEA model impose upper and lower bounds on the weights to eliminate certain drawbacks associated with unrestricted weights. These variants are called weight restriction DEA models. Most weight restriction DEA models suffer from a drawback that the weight bound values are uncertain because they are determined based on either incomplete information or the subjective opinion of the decision-makers. Since the efficiency scores calculated by the DEA model are sensitive to the values of the bounds, the uncertainty of the bounds gets passed onto the efficiency scores. The uncertainty in the efficiency scores becomes unacceptable when we consider the fact that the DEA results are used for making important decisions like allocating funds and taking action against inefficient units. In order to minimize the effect of the uncertainty in bound values on the decision-making process, we propose to explicitly incorporate the uncertainty in the modeling process using the concepts of fuzzy set theory. Modeling the imprecision involves replacing the bound values by fuzzy numbers because fuzzy numbers can capture the intuitive conception of approximate numbers very well. Amongst the numerous types of weight restriction DEA models developed in the research, two are more commonly used in real-life applications compared to the others. Therefore, in this research, we focus on these two types of models for modeling the uncertainty in bound values. These are the absolute weight restriction DEA models and the Assurance Region (AR) DEA models. After developing the fuzzy models, we provide implementation roadmaps for illustrating the development and solution methodology of those models. We apply the fuzzy weight restriction models to the same data sets as those used by the corresponding crisp weight restriction models in the literature and compare the results using the two-sample paired t-test for means. We also use the fuzzy AR model developed in the research to measure the performance of a newspaper preprint insertion line. / Master of Science

Submitted by Secretaria Pós de Produção (tpp@vm.uff.br) on 2017-07-27T18:57:44Z No. of bitstreams: 1 D2016 - Gustavo Naciff de Andrade.pdf: 2452194 bytes, checksum: f8401611b3a2637e99e0b74cf7192ddd (MD5) / Made available in DSpace on 2017-07-27T18:57:44Z (GMT). No. of bitstreams: 1 D2016 - Gustavo Naciff de Andrade.pdf: 2452194 bytes, checksum: f8401611b3a2637e99e0b74cf7192ddd (MD5) / Medir a eficiência levando em consideração as preferências de um decisor estabelecidas a priori. Para tanto propõe-se a integração da modelagem de Análise Envoltória de Dados (DEA) e a metodologia multicritério Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) através de um problema de programação linear integrado. São propostas duas abordagens de integração. A primeira delas, denominada DEAMACBETH, agrega os outputs do modelo usando a lógica MACBETH. Nesta abordagem, quando se realiza a transformação característica de MACBETH nos pesos dos outputs, chegase aos mesmos pesos das trocas que o modelo multicritério sugeriria para uma mesma matriz de julgamentos. A segunda abordagem deriva da primeira, mas busca utilizar as restrições de MACBETH como restrições aos pesos em DEA, por esta razão é denominada DEAMACBETH-WR (WR – Weight Restrictions). É proposto um algoritmo que utiliza um parâmetro do modelo anterior para possibilitar uma flexibilização na razão dos pesos do modelo permitindo uma maior flexibilidade na atribuição aos pesos do que o modelo DEAMACBETH. Por fim, é apresentado um estudo de caso em que se busca avaliar o portfólio de investimentos em projetos por distribuidora no âmbito do Programa de Eficiência Energética (PEE) da ANEEL. Os resultados evidenciam como diferentes matrizes de julgamento conduzem a rankings diferentes de distribuidoras para ambas as abordagens desenvolvidas. / This study aims to develop a new methodology to measure the efficiency taking into account the preferences of a decision maker. It is proposed the integration of Data Envlopment Analysis (DEA) and the multicriteria methodology Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) through an integrated linear programming problem. Two approaches to this integration are proposed. The first, called DEA-MACBETH, aggregates the outputs of the model using MACBETH logic. This fact is proven when performing the transformation, characteristic of MACBETH, in the weights of outputs and comes up to same swing weights that the multi-criteria model would suggest to the same judgments matrix. The second approach is derived from the first but uses MACBETH restrictions such as restrictions on weights in DEA. For this reason this second approach is referred DEA-MACBETH-WR (WR - Weight Restrictions). It is proposed an algorithm which uses a previous model parameter to allow flexibility in the weights in comparison to the DEA-MACBETH model. Finally, it is presented a case study in which the objective is to evaluate the portfolio of investments for brazilians distributors in Energy Efficiency Program Project (EEP). The results show how different judgment matrix can lead to different rankings of distributors for the developed approaches.

ABSTRACT A DEA-BASED APPROACH TO RANKING MULTI-CRITERIA ALTERNATIVES Tuncer, Ceren M.Sc., Department of Industrial Engineering Supervisor: Prof. Dr. Murat K&ouml / ksalan August 2006, 88 pages This thesis addresses the problem of ranking multi-criteria alternatives. A Data Envelopment Analysis (DEA)-based approach, the Method of the Area of the Efficiency Score Graph (AES) is proposed. Rather than assessing the alternatives with respect to the fixed original alternative set as done in the existing DEA-based ranking methods, AES considers the change in the efficiency scores of the alternatives while reducing the size of the alternative set. Producing a final score for each alternative that accounts for the progress of its efficiency score, AES favors alternatives that manage to improve quickly and maintain high levels of efficiency. The preferences of the Decision Maker (DM) are incorporated into the analysis in the form of weight restrictions. The utilization of the AES scores of the alternatives in an incremental clustering algorithm is also proposed. The AES Method is applied to rank MBA programs worldwide, sorting of the programs is also performed using their AES scores. Results are compared to another DEA-based ranking method. Keywords: Ranking, data envelopment analysis, weight restrictions.