A novel method for solving data envelopment analysis problems with weak ordinal data using robust measures

Abstract

The efficiency measurement with traditional data envelopment analysis (DEA) requires precise input and output data. However, the input and output data is imprecise in many real-world problems. Various imprecise methods are developed to estimate the lower and upper bound efficiency scores in the presence of interval and weak ordinal data. We show the existing methods provide an estimation of the lower or upper bound efficiency score and cannot find their exact values in the presence of weak ordinal data. As a result, the ranking of decision making units (DMUs) may not be reliable since they are based on estimated efficiency scores. We propose a pair of DEA models to find the lower and upper bound efficiency scores. We prove the proposed models can find the exact values of the lower and upper bound efficiency scores in the presence of weak ordinal data. However, these exact values depend on a set of parameters in the presence of ordinal data. Therefore, we further propose a novel measure, fathoming the robustness of the efficiency function for the parameter space, to select the best practice DMUs in the presence of imprecise data. We present a real-world application in the space industry to demonstrate the applicability and superiority of the proposed method over the existing methods.