Reallocation of Resources to Preserve Relative Efficiencies: Inverse CCR Model

Abstract

This paper is concerned with the inverse Data Envelopment Analysis (inverse DEA) when the production function exhibits constant returns to scale (inverse CCR). The inverse CCR problem is the reallocation of input resources to a particular decision-making unit (DMU) given that output values of the DMU are changed and relative efficiencies of all DMUs should remain the same. We focus on the problem where increases of some outputs and decreases of other outputs of the considered DMU can be considered at the same time. The proposed inverse CCR model is a multi-objective nonlinear programming problem (MONLP). We show that a Pareto solution to the MONLP can be obtained from solving a proposed linear programming model. We also investigate the relationship between the changes in input and output values of the particular DMU.