This　paper　studies　an　acquisition　and　remanufacturing　problem　in　a　market-driven　multi-product　remanufacturing　system,　where　the　remanufacturer　acquires　multiple　used　products　(cores)　of　highly　variable　quality　under　independently　uncertain　demand　and　carbon　emissions　regulation.　In　order　to　balance　between　the　environmental　and　economic　benefit,　the　problem　is　formulated　as　a　nonlinear　programming　model　in　presence　of　the　quality　variability　of　cores　and　carbon　tax　scheme,　subject　to　budget　and　risk　constraints.　Since　the　average　cost　of　the　remanufactured　products　is　independent　of　the　remanufacturing　quantity,　the　model　is　then　decomposed　into　two　separated　sub-problems,　namely　the　remanufacturing　problem　and　the　acquisition　problem.　In　the　remanufacturing　problem,　the　optimal　remanufacturing　policies,　including　the　optimal　remanufacturing　cost　thresholds　and　the　optimal　remanufacturing　rate,　are　derived.　In　the　acquisition　problem,　the　optimal　policies　of　core　portfolio,　acquisition　quantities,　and　remanufacturing　quantities　can　be　derived.　The　acquisition　problem,　viewed　as　an　extended　Multi-Product　Newsvendor　Problem　(MPNP),　is　a　convex　optimization　problem.　Furthermore,　a　two-tier　bisection　method　with　polynomial　computational　complexity　can　be　developed　to　obtain　the　optimal　policies　based　on　the　Karush-Kuhn-Tucker　(KKT)　conditions.　Finally,　numerical　experiments　are　provided　to　show　the　application　of　the　model　and　the　effect　of　the　quality　variability.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.