Given　a　set　of　n　points　in　Rd　with　nonnegative　weights,　we　consider　the　weighted　rectilinear　min-sum　facility　problem　to　minimize　the　sum　of　weighted　rectilinear　distance　between　the　given　points　and　a　new　added　point.　We　present　four　simple　algorithms　for　the　weighted　rectilinear　min-sum　facility　location　problem.　The　computational　experiments　demonstrate　that　the　achieved　results　are　not　only　of　theoretical　interest,　but　also　that　the　techniques　developed　may　actually　lead　to　considerably　faster　algorithms.　©2010　IEEE.