The　input　of　the　universal　facility　location　problem　includes　a　set　of　clients　and　a　set　of　facilities.　Our　goal　is　to　find　an　assignment　such　that　each　client　is　assigned　while　the　total　connection　and　facility　cost　is　minimized.　Here　the　connection　cost　is　proportional　to　the　distance　between　each　client　and　its　assigned　facility,　thus　metric.　The　facility　cost　is　a　nondecreasing　function　with　respect　to　the　total　number　of　clients　assigned　to　the　facility.　The　universal　facility　location　problem　is　NP-hard　since　it　generalizes　several　classical　facility　location　problems.　Our　work　considers　the　universal　facility　location　problem　with　linear　penalties,　a　generalized　version　of　the　universal　facility　location　problem.　Here　each　client　can　be　rejected　for　service　with　certain　penalty　cost.　Thus　we　have　to　consider　penalty　cost　other　than　total　connection　and　facility　cost　in　our　objective　function.　Based　on　local　search　method,　we　present　a　(5.83+ϵ)-approximation　algorithm　for　this　problem.　©　2017