Development of a new cost PPS and decomposition of observed actual cost for DMU in a non-competitive space in DEA

¹ Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran
² Department of Mathematics, Tehran Center Branch, Islamic Azad University, Tehran, Iran
³ Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran

^* Corresponding author: r.fallahnejad@khoiau.ac.ir, rezafallahnejad120@gmail.com

Received: 13 October 2018
Accepted: 20 June 2019

Abstract

Data Envelopment Analysis (DEA) is an appropriate tool for estimating various types of efficiency such as cost efficiency. There are two different sates in cost spaces; in the first space prices are equal for all Decision Making Units (DMUs) which is competitive space, and in the second space prices are different form one DMU to another; this is known as non-competitive space. The present paper introduces a new method to assess Cost Efficiency (CE), Revenue Efficiency (RE) and Profit Efficiency (PE) in a non-competitive space. The present paper also proposes a Production Possibility Set (PPS) in which DMUs are evaluated based on both their own prices and the prices of other DMUs in non-competitive space. Moreover, a new decomposition is provided for observed actual cost DMUs based on the cost efficiency model and the proposed PPS, thus the observed actual cost can be shown by summation of several technical, price and allocative efficiency (AE) losses. The biggest advantage of this method comparing to the previous methods is that passive the developed cost efficiency and the cost Production Possibility Set has been developed and the performed decomposition is more accurate; this is because the new inefficiency sources are defined and added to this new decomposition. Therefore, it includes more inefficient sources.