en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <span style="font-size:11pt"><span style="line-height:107%"><span aptos="" style="font-family:"><span style="font-size:12.0pt"><span style="line-height:107%"><span new="" roman="" style="font-family:" times="">Measuring capacity utilization is an important aspect among processes in order to determine overcapacity or undercapacity. Furthermore, in many situations, the convexity and homogeneity properties are not satisfied. Accordingly, in this paper, meta-frontier free disposal hull (FDH) frameworks are proposed to estimate output-oriented and input-oriented capacity utilization (CU) rates of firms under nonconvexity property and heterogeneity of technology. Also, the introduced technique is applied to assess capacity utilization of some Iranian hospitals. The findings show the presented approach is beneficial to measure capacity utilization rates of systems in the presence of nonconvexity and heterogeneity.</span></span></span></span></span></span><br> &nbsp; Capacity utilization, Free disposal hull, Meta-frontier, DEA. 120 131 http://iors.ir/journal/browse.php?a_code=A-10-304-9&slc_lang=en&sid=1 F. Ahmadi siahmard@iau.ir 00031947532846003152 00031947532846003152 No Department of Mathematics, Ra.C., Islamic Azad University, Rasht, Iran S. Kordrostami sohrab.kordrostami@iau.ac.ir 00031947532846003153 00031947532846003153 Yes Department of Mathematics, La. C., Islamic Azad University, Lahijan, Iran M. Mirzaei Chalakei Mo.mirzaei@iau.ac.ir 00031947532846003154 00031947532846003154 No Department of Mathematics, Ast. C., Islamic Azad University, Astaneh Ashrafieh, Iran L. Khoshandam LKhoshandam@iau.ac.ir 00031947532846003155 00031947532846003155 No Department of Mathematics, Ra.C., Islamic Azad University, Rasht, Iran