Preserve the Relative Efficiency Values: An Inverse Data Envelopment Analysis with Imprecise Data

Abstract

Data envelopment analysis (DEA) measures the relative efficiency of a set of decision-making units (DMUs). With the advent of DEA models, inverse DEA is applied to modify the inputs and outputs of DMUs without affecting their efficiency. InvDEA models are applied when the decision makers need to change the input-outputs of the DMUs to a certain level without affecting their efficiency. InvDEA models are extended when the input-output data are imprecise and available in the intervals form. However, regarding uncertainty, complete information about the input-output data is not available in many real world applications. To address this problem, this study deals with the InvDEA problem in an uncertain environment. Therefore, two multi-objective linear programming (MOLP) models are proposed to estimate the required upper/lower inputs, producing requested outputs and preserving the efficiency scores. The proposed models preserve the upper/lower efficiency scores of all considered DMUs. A numerical example illustrates the proposed methodology.