A Neural Network approach for Non-parametric Performance Assessment

Data Envelopment Analysis (DEA) is the most popular non-parametric method for the efficiency assessment of homogeneous units. In this paper, we develop a novel approach, which integrates DEA with Artificial Neural Networks (ANNs) to accelerate the evaluation process and reduce the computational burden. We employ ANNs to estimate the efficiency scores of the milestone DEA models. The relative nature of DEA is considered in our approach by assuring that the DMUs used for training the ANNs are first evaluated against the efficient set. The ANNs employed in our approach estimate accurately the DEA efficiency scores. We validate our approach by conducting a series of experiments based on different data generation processes and number of inputs and outputs. Also, these estimated efficiency scores satisfy the properties of the fundamental DEA models. Thus, our approach can be employed for large scale assessments where the traditional DEA methods are rendered impractical.

I. Introduction

Data Envelopment Analysis (DEA) is the leading nonparametric method for performance measurement of a set of homogeneous entities, called Decision Making Units (DMUs), which use multiple inputs to produce multiple outputs. In econometric approaches an explicit production function is assumed, with the parameters of this function being estimates to fit the observations. On the contrary, the performance evaluation in the context of DEA is based only on the observed data of the units, and none pre-defined assumption about the functional relationship of the inputs and outputs is required. The underlying mathematical method that enables DEA to determine the efficiency of each DMU is linear programming. Also, different assumptions about the orientation of the analysis and the returns to scale can be imposed to the efficiency assessment. The two milestone DEA models are the CCR [8] under the constant returns to scale (CRS) assumption and the BCC [7] variable returns to scale (VRS) respectively. In addition, DEA uncovers the sources of inefficiency and provides directions for improving the inefficient DMUs. These characteristics render DEA an attractive method, which has received great attention from the research community. The application field of DEA is wide as it has been utilized in various sectors such as health care, agriculture, transportation, education, energy, finance, etc.