In　this　paper,　we　study　approximation　algorithms　for　two　supply　chain　network　design　problems,　namely,　the　warehouse-retailer　network　design　problem　(WRND)　and　the　stochastic　transportation-inventory　network　design　problem　(MIND).　These　two　problems　generalize　the　classical　uncapacitated　facility　location　problem　by　incorporating,　respectively,　the　warehouse-retailer　echelon　inventory　cost　and　the　warehouse　cycle　inventory　together　with　the　safety　stock　costs.　The　WRND　and　the　STIND　were　initially　studied,　respectively,　by　Teo　and　Shu　(Teo　CP,　Shu　J　(2004)　Warehouse-retailer　network　design　problem.　Oper.　Res.　52(3):396-408)　and　Shu　et　al.　(Shu　J,　Teo　CP,　Shen　ZJM　(2005)　Stochastic　transportation-inventory　network　design　problem.　Oper.　Res.　53(1):48-60),　where　they　are　formulated　as　set-covering　problems,　and　column-generation　algorithms　were　used　to　solve　their　linear　programming　relaxations.　Both　problems　can　be　regarded　as　special　cases　of　the　so-called　facility　location　with　submodular　facility　costs　proposed　by　Svitkina　and　Tardos　(Svitkina　Z,　Tardos　E　(2010)　Facility　location　with　hierarchical　facility　costs.　ACM　Trans.　Algorithms　6(2),　Article　No.　37),　for　which　only　a　logarithmic-factor　approximation　algorithm　is　known.　Our　main　contribution　is　to　obtain　efficient　constant-factor　approximation　algorithms　for　the　WRND　and　the　STIND,　which　are　capable　of　solving　large-scale　instances　of　these　problems　efficiently.