Given　a　set　X　of　n　points　in　a　metric　space　and　a　radius　R,　we　consider　the　combining　version　of　k-center　and　k-median　which　is　with　the　same　objective　as　k-median,　but　with　the　constraint　that　any　x　in　X　is　assigned　to　a　center　within　the　range　R.　In　this　paper,　we　propose　a　bicriteria　approximation　algorithm　achieving　a　bicriteria　approximation　ratio　of　(3+ε,7),　by　incorporating　local　search　with　the　technology　of　finding　key　balls　with　consequent　center　exchanges　therein.　Compared　to　the　state-of-the-art　approximation　ratio　of　(8, 4)　that　is　based　on　an　LP　formulation　for　k-median,　we　improve　the　ratio　of　the　total　distance　from　8　to　3+ε　at　the　price　of　compromising　the　ratio　of　radius　from　4　to　7.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2024.