University of IsfahanTransactions on Combinatorics2251-865713420241201The inverse 1-median problem on a tree with transferring the weight of vertices3353502776710.22108/toc.2023.136964.2047ENTahereSayarFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran.JafarFathaliFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran0000-0003-1397-8529MojtabaGhiyasiDepartment of Management and Accounting, Faculty of Industrial Engineering and Management Sciences,
Shahrood University of Technology, Shahrood, Iran.Journal Article20230225In this paper, we investigate a case of the inverse 1-median problem on a tree by transferring the weights of vertices which has not been raised so far. This problem considers modifying the weights of vertices via transferring weights of the vertices with the minimum cost such that a given vertex of the tree becomes the 1-median with respect to the new weights. A linear programming model is proposed for this problem. The applicability and efficiency of the presented model are shown in numerical examples and a real-life problem dealing with transferring users in a social network.https://toc.ui.ac.ir/article_27767_8be004d2de59d9bb64f37acecec2f724.pdf