Estimating Relative Efficiency of DMU: Pareto Principle and Monte Carlo Oriented DEA Approach

The traditional data envelopment analysis (DEA) models treat a decision making unit (DMU) as a “black box”, which is often criticized for not considering the inner production mechanism of a production system. The network DEA models developed to overcome this deficiency by considering the internal structure of a DMU have recently gained popularity. The inner data, however, are not generally available for real application purposes. This paper, on one hand, addresses the problem with the traditional DEA for not considering the inner structure and, on the other, with the network models for missing inner data in parallel production settings. Procedures built on managerial information of production processes, as characterized by the Pareto principle, are presented that consider the inner production mechanism as well as the data availability in a reliable way. Firstly, the production activities of a DMU are classified into a core business unit (CBU) and a non-core business unit (NCBU). Secondly, the internal information related to inputs/outputs is assumed to be available for the DMU under evaluation; whereas for the other DMUs, this data is generated by using the Pareto principle. In addition, the Monte Carlo method, also known as the parametric bootstrap, is applied to estimate the efficiency of the DMU. A numerical example illustrates the proposed method.