Pesquisa Operacional (2012) 32(1): 21-29
© 2012 Brazilian Operations Research Society
Printed version ISSN 0101-7438 / Online version ISSN 1678-5142
www.scielo.br/pope
A DEA MODEL WITH A NON DISCRITIONARY VARIABLE
FOR OLYMPIC EVALUATION
Jo˜ ao Carlos C.B. Soares de Mello
*
, Lidia Angulo-Meza
and F´ abio Gomes Lacerda
Received December 10, 2009 / Accepted February 15, 2011
ABSTRACT. In recent years, a lot of work has been done dealing with alternative performance rankings
for the Olympic Games. Almost all of these works use Data Envelopment Analysis (DEA). Generally
speaking, those works can be divided into two categories: Pure rankings with unitary input models and
relative rankings with classical DEA models; both output oriented. In this paper we introduce an approach
taking into account the number of athletes as a proxy to the country investment in sports. This number is
an input for a DEA model, and the other input is the population of the country. We have three outputs,
the number of gold, silver and bronze medals earned by each country. Contrary to the usual approach in
the literature, our model is not output oriented. It is a non-radial DEA model oriented to the “number of
athletes” input, as our goal is not a countries’ ranking. We intend to analyse whether the number of athletes
competing for each country accords with the number of won medals. For this analysis, we compare each
country with its benchmarks. The Decision Making Units (DMU) are all the countries participating in the
Beijing Olympic Games, including those that did not earn a single medal. We use a BCC model and we
compare each DMU’s target with the number of athletes who have won, at least one medal.
Keywords: Data Envelopment Analysis, olympic games, sport evaluation.
1 INTRODUCTION
Performance evaluation has been widely studied in sport for the last 25 years (Nevill et al., 2008).
In the case of the Olympic Games the rank of the nations is traditionally carried out with the so-
called Lexicographic Multicriteria Method (Lins et al., 2003). In this very paper the drawbacks
of the Lexicographic Method are pointed out and a new ranking is suggested.
There are already some other approaches using Data Envelopment Analysis (Charnes et al.,
1978). The very first one was proposed by Lozano et al. (2002). They used population and
GNP as inputs and the medals as outputs. In a similar approach, Lins et al. (2003) built a new
*Corresponding author
Departamento de Engenharia de Produc ¸˜ ao, Universidade Federal Fluminense. E-mail: jcsmello@pq.cnpq.br