Efficiency evaluation of a small number of DMUs: an approach based on Li and Reeves's model

This paper deals with the evaluation of Decision Making Units (DMU) when their number is not large enough to allow the use of classic Data Envelopment Analysis (DEA) models. To do so, we take advantage of the TRIMAP software when used to study the Li and Reeves MultiCriteria DEA (MCDEA) model. We introduce an evaluation measure obtained with the integration of one of the objective functions along the weight space. This measure allows the DMUs joint evaluation. This approach is exemplified with numerical data from some Brazilian electrical companies.<br>Este artigo trata da avaliação de Unidades Produtivas (Decision Making Units - DMUs) quando seu número é inferior ao recomendado na Análise Envoltória de Dados (Data Envelopment Analysis - DEA). Para isso é explorado o uso do software TRIMAP no modelo MCDEA (MultiCriteria DEA) de Li e Reeves. É proposto um índice de avaliação de desempenho baseado nos valores assumidos por uma das funções objetivo do modelo MCDEA. Estes valores, obtidos pelo TRIMAP, são integrados ao longo de todo o espaço dos pesos. O índice obtido permite uma avaliação de conjunto das DMUs avaliadas. O modelo é ilustrado com um exemplo numérico de avaliação de empresas distribuidoras de energia elétrica

Use of ordinal multi-criteria methods in the analysis of the Formula 1 World Championship

Sporting activities apply various multi-criteria (and multi-decision maker) methods in their championship regulations. In the majority of cases, the organizers are not aware that they are using them and indeed often apply them incorrectly. Variations of the Borda voting and lexicographic methods are among those most widely used. In the case of the Formula 1 World Championship, a variation of the Borda method is employed. This article shows that some of the problems that occurred during recent seasons are a result of the use of this method with consequent aggravation of the inherent distortions. Furthermore, the use of the Condorcet method is suggested as an alternative. Its limitations are shown, as well as how to overcome them by employing the Copeland method. Lastly, an analysis of the results of the 2002 championship is conducted

Integração entre o ensino de cálculo e o de pesquisa operacional How to teach calculus and operational research in an integrated way

Pretende-se mostrar neste trabalho como é possível ensinar, de forma integrada, as disciplinas de Cálculo Diferencial e de Pesquisa Operacional. Para tal são necessárias pequenas mudanças na forma como o Cálculo é tradicionalmente ensinado, mas grandes mudanças no ensino tradicional de Pesquisa Operacional. Com estas mudanças, Pesquisa Operacional pode cumprir o papel de disciplina integradora, fazendo a transição entre os ciclos básico e profissional no curso de Engenharia de Produção.<br>The aim of this paper is to show the possibilities of integration between the teaching of Differential Calculus and Operational Research. The integration is obtained with some small changes in the way that calculus is traditionally presented and some major changes in Operational Research classes. We show that, with the above-mentioned changes, Operational Research can play an important role in the transition between the first half and the last part of the Production Engineering courses