Studies of some duality properties in the Li and Reeves model

Maria Cecilia de Carvalho Chaves, João Carlos C B Soares de Mello and Lidia Angulo-Meza
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Maria Cecilia de Carvalho Chaves: Rio de Janeiro Federal University, Rio de Janeiro, Brazil
João Carlos C B Soares de Mello: Fluminense Federal University, Niterói, Brazil
Lidia Angulo-Meza: Fluminense Federal University, Niterói, Brazil

Journal of the Operational Research Society, 2016, vol. 67, issue 3, 474-482

Abstract: 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.

Date: 2016
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