en عمومى General پژوهشي Research paper <div style="text-align: justify;"><span class="fontstyle0">In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse case of facility location problem with equality measure considers modifying the weights of vertices with a given budget constraint, such that the difference between the maximum and minimum weights of vertices allocated to the given facilities is reduced as much as possible. Two algorithms with time complexity </span><span class="fontstyle2">O</span><span class="fontstyle0">(</span><span class="fontstyle2">nlogn</span><span class="fontstyle0">) are presented for the inverse and reverse 2-facility location problems with equality measures. Computational results show their superiority with respect to the linear programming models.</span></div> Inverse facility location, Reverse facility location, Balanced allocation, Equality measure. 211 225 http://ijmsi.ir/browse.php?a_code=A-10-312-2&slc_lang=en&sid=1 Morteza Nazari mnazari_ms65@yahoo.com 100319475328460010036 100319475328460010036 No Faculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran Jafar Fathali fathali@shahroodut.ac.ir 100319475328460010037 100319475328460010037 Yes Faculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran