Most　existing　facility　location　models　assume　that　the　facility　cost　is　either　a　fixed　setup　cost　or　made　up　of　a　fixed　setup　and　a　problem-specific　concave　or　submodular　cost　term.　This　structural　property　plays　a　critical　role　in　developing　fast　branch-and-price,　Lagrangian　relaxation,　constant　ratio　approximation,　and　conic　integer　programming　reformulation　approaches　for　these　NP-hard　problems.　Many　practical　considerations　and　complicating　factors,　however,　can　make　the　facility　cost　no　longer　concave　or　submodular.　By　removing　this　restrictive　assumption,　we　study　a　new　location　model　that　considers　general　nonlinear　costs　to　operate　facilities　in　the　facility　location　framework.　The　general　model　does　not　even　admit　any　approximation　algorithms　unless　P　=　NP　because　it　takes　the　unsplittable　hard-capacitated　metric　facility　location　problem　as　a　special　case.　We　first　reformulate　this　general　model　as　a　set-partitioning　model　and　then　propose　a　branch-and-price　approach.　Although　the　corresponding　pricing　problem　is　NP-hard,　we　effectively　analyze　its　structural　properties　and　design　an　algorithm　to　solve　it　efficiently.　The　numerical　results　obtained　from　two　implementation　examples　of　the　general　model　demonstrate　the　effectiveness　of　the　solution　approach,　reveal　the　managerial　implications,　and　validate　the　importance　to　study　the　general　framework.