In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.Keywords: Data Envelopment Analysis; Multi-objective; MCDEA; Duality; Benchmarks.
IntroductionThe MultiCriteria Data Envelopment Analysis (MCDEA) model is classified by Climaco et al (2008) as a DEA model with additional objective functions and by Angulo-Meza and Lins (2002) as an increasing discrimination method with no a priori information from the decision maker. This model was proposed by Li and Reeves (1999), which takes into account two additional objective functions, called the minisum and minimax efficiency. This model was introduced to deal with two common problems in DEA models, poor discriminations among DMUs, and unreal distribution of inputs and outputs weights. However this model does not provide an efficiency index for all DMUs, nor targets and benchmarks. Some efficiency indexes based on the MCDEA model were obtained by Soares de Mello et al (2009) and used by Climaco et al (2010).A variation of the MCDEA was presented by Bal et al (2010). However, even these
Maria Cecilia de Carvalho ChavesJoão Carlos C. B.
Soares de Mello Lidia Angulo-MezaJournal of the Operational Research Society doi:10.1057/jors.2015.73 2 articles do not cover two important pieces of management information supplied by DEA models: the benchmarks and the targets for inefficient DMUs. In standard DEA, these targets and benchmarks are obtained using the envelopment model, which is in fact the dual formulation of the multiplier model. There are multiobjective DEA models that, despite not being able to provide efficiency indexes, provide benchmarks for the inefficient DMUS (Lins et al. 2004;Quariguasi Frota Neto and Angulo-Meza 2007).However, these models have a different structure than the Li and Reeve's model. This paper is in the same line of Gomes Jr et al (2013) which provides an efficiency index for models designed to determine benchmarks. Now, where are dealing with an inverse situation: we want to obtain benchmarks in a model designed to find efficiency indexes.In both situations, the aim is to obtain full information from models that originally provide only partial information.Therefore to determine benchmarks for inef...