Reza Fallahnejad - Department of mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran.
Sanaz Asadi Rahmati - Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran.
Kayvan Moradipour - Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran.

To evaluate the performance and estimate the efficiency of Decision-Making Units (DMUs) in Data Envelopment Analysis (DEA), the available data are used. These data are usually divided into two categories of inputs and outputs based on their natures. If the price data is also available for inputs, it is necessary to calculate another type of the efficiency called Cost Efficiency (CE). Since the efficiency of units in such a framework is depended on the both quantities of inputs and outputs and also the prices of inputs, it is important to find the sources of cost inefficiency related to each of the factors and plans to address them. In this paper, we intend to present a new decomposition of CE and observed cost versus optimal cost, which are raised from each of the factors involved in the cost inefficiency, in a non-competitive pricing environment which the input price vector for different DMUs can be different. Moreover, for the first time, in parallel with using the PPS based on input and output quantities and introducing some cost inefficiency factors related to this set, we will introduce new sets called price and cost production sets that the first is based on the prices of inputs and output factors, and the second is based on the optimal vectors of inputs and prices obtained from two previous PPS, and then we will introduce other factors of cost inefficiency in the sets. Accordingly, new decomposition for cost inefficiencies will be presented. Also, in the previous analyzes, congestion inefficiency has not been considered as one of the important factors in cost inefficiency. In this study, we also intend to consider the impact of this factor on CE.

Data Envelopment Analysis, Cost efficiency, Non-Competitive Environment, Cost PPS, Cost decomposition, Congestion