Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

Amixed integer linear model for selecting the best decisionmaking unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying themost efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output informationwithout the need of specifying any assurance regions for input and outputweights to avoid zeroweights, canmake correct selectionswithout being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of themost efficientDMU. Thepotential applications of theproposed alternativeMILPmodels and their effectiveness are illustrated with four numerical examples. 2011 Elsevier Ltd. All rights reserved.