A　carbon　tax,　which　has　been　implemented　in　several　countries,　is　a　cost-effective　scheme　for　reducing　carbon　emission　and　developing　sustainable　supply　chains.　Two　problems,　how　to　make　the　optimal　decision　on　order　quantity　and　how　to　select　appropriate　suppliers　for　a　manufacturer,　are　studied　in　this　paper　in　consideration　of　a　carbon　tax.　For　the　first　problem,　a　dynamic　programming　model　is　developed　to　study　the　impact　of　the　carbon　tax　on　calculating　the　optimal　order　quantity.　In　reality,　the　manufacturer　could　choose　a　traditional　or　a　greener　supplier.　The　greener　supplier　is　relatively　expensive　but　yields　lower　emissions.　To　obey　the　emission　regulations,　the　manufacturer　should　pay　for　the　cost　which　is　incurred　by　carbon　emission.　Firstly,　in　this　paper,　the　expected　emission　cost　is　formulated,　then,　the　structural　properties　of　the　model　are　derived.　In　particular,　the　optimal　order　quantity　is　characterized　to　minimize　the　expected　total　discounted　cost.　In　addition,　the　effective　range　of　the　carbon　tax　is　established　to　assist　government　to　setup　a　reasonable　carbon　tax　for　a　certain　industry.　For　the　second　problem,　a　supplier　evaluation　procedure　is　proposed　to　select　appropriate　suppliers　to　satisfy　the　random　market　demand　for　the　manufacturer.　A　numerical　example　from　the　metal　industry　is　taken　to　illustrate　the　properties　of　the　model　and　the　procedure　of　supplier　evaluation.　Finally,　possible　extensions　of　the　model　are　discussed.　©　2017　Elsevier　Ltd