S Kazem nadi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
M Rostamy-malkhalifeh - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

In classical models of data envelopment analysis, it is assumed that the status of all indices is clear in terms of whether the index is an input or output; while in some real cases there are indicators that can be both an input indicator and output indicator which means that their situation is not clear. In these cases, some models have been developed to evaluate efficiency which determines their status and givethe amount of efficiency. Another application of data envelopment analysis is the calculation of cost, income, and profit efficiency. In cost efficiency, the efficient units are those which use the lowest cost to buy inputs to produce outputs, and in income efficiency, efficient units are those which earn the most revenue from output sales by using input. This paper aims to calculate the cost, income, and profit efficiencywith free indicators that can either be an input indicator or an output indicator. So, we designed models that, in addition to identifying the status of free indicators, gave the most cost, revenue and profit efficiency and finally a numerical example is presented.

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran