A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems

¹ Department of Mathematics, South Tehran Branch, Islamic Azad University Tehran, Tehran, Iran
² Department of Mathematics, Science and Research Branch, Islamic Azad University Tehran, Tehran, Iran
³ Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Qaemshahr, Iran

^* Corresponding author: farhad@hosseinzadeh.ir

Received: 4 June 2018
Accepted: 5 December 2019

Abstract

Two-stage production systems are often encountered in many real applications where the production process is divided into two processes. In contrast to the conventional data envelopment analysis (DEA) models, two-stage DEA models take the operations of the internal processes into account. A number of studies have used two-stage DEA models in order to evaluate the performance of decision making units (DMUs) having a network structure. In this paper, we use a non-radial DEA model called the network slacks-based measure (NSBM) model to measure the efficiency of a system with a multi-period two-stage structure. Then we describe the properties of the proposed model in details. Moreover, we shall decompose the overall efficiency of the system over a number of time periods as a weighted average of the efficiency in each period. The efficiency of the stages, in respect to the entire periods shall be decomposed in terms of the weighted average efficiency of the stages in each period. Finally, the real data of Mellat bank branches in Tehran extracted from extant literature is used to illustrate the proposed approach.