High　uncertainty　and　variability　of　acquirable　cores　can　lead　to　some　difficulties　of　operations　management　in　the　remanufacturing　process.　Two　acquisition　models　with　quantity　discount　and　carbon　tax　scheme　were　established　to　analyze　the　effect　of　quality　variability　and　condition　uncertainty　and　to　reduce　these　difficulties.　In　the　first　model,　quality　variability　was　considered.　The　optimal　acquisition　policy　was　determined　by　a　single　closed-form　expression　because　the　average　cost　of　remanufactured　products　is　independent　of　the　acquisition　quantity　for　a　given　discount　segment.　In　the　second　model,　both　quality　variability　and　condition　uncertainty　were　considered.　The　properties　of　the　model　were　analyzed,　and　a　single　algorithm　was　developed　to　obtain　the　optimal　acquisition　policy　based　on　the　bisection　method.　Finally,　numerical　simulation　examples　were　provided　to　explore　the　effect　of　quantity　discount　on　the　optimal　acquisition　policy.　Results　show　that　the　quantity　discount　schedule　impels　remanufacturers　to　acquire　more　cores　and　enhances　the　chances　of　remanufacturers　to　select　the　best　cores.　Moreover,　the　total　expected　cost　decreases,　especially　in　the　case　with　both　quality　variability　and　condition　uncertainty.　The　proposed　model　can　effectively　solve　the　acquisition　problem　in　remanufacturing　systems.