other Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original Due to the changes of performance measures, a vital aspect for decision makers is finding optimal scale sizes of entities. Moreover, there are undesirable measures in many investigations. In the existing data envelopment analysis (DEA) approaches, optimal scale sizes (OSSs), average-cost efficiency (ACE) and average-revenue efficiency (ARE) of decision making units (DMUs) with desirable measures under strong disposability have been estimated while undesirable factors are presented in many real world examinations. Accordingly, in this research, OSSs and ARE of DMUs with undesirable outputs are addressed under managerial disposability. ARE is defined as the composite of scale and output allocative efficiencies under managerial disposability. To illustrate in detail, a two-stage DEA-based approach is rendered to estimate ARE and OSSs in the presence of undesirable outputs. A numerical example and an illustrative case are given to explain the proposed approach in this study. Data envelopment analysis, average-revenue efficiency, optimal scale size, undesirable outputs, managerial disposability. 146 157 http://iors.ir/journal/browse.php?a_code=A-10-1422-51&slc_lang=other&sid=1 Monireh Jahani Sayyad Noveiri Monireh Jahani Sayyad Noveiri monirehjahani@yahoo.com 1111111111 1111111111 No Lahijan Branch, Islamic Azad University, Lahijan, Iran Lahijan Branch, Islamic Azad University, Lahijan, Iran Sohrab Kordrostami Sohrab Kordrostami sohrabkordrostami@gmail.com 1111111111 1111111111 Yes Lahijan Branch, Islamic Azad University, Lahijan, Iran Lahijan Branch, Islamic Azad University, Lahijan, Iran Somayye Karimi Omshi Somayye Karimi Omshi baranbena2014@gmail.com 1111111111 1111111111 No Lahijan Branch, Islamic Azad University, Lahijan, Iran Lahijan Branch, Islamic Azad University, Lahijan, Iran