Reverse　logistics　network　involves　significant　inherent　uncertainties,　which　cannot　be　completely　characterized　because　of　a　lack　of　adequate　historical　data.　In　this　study,　a　multi-product　and　multi-period　interval　programming　model　was　developed　on　the　basis　of　partial　information　to　design　an　effective　reverse　logistics　network.　In　addition,　the　trade-offbetween　economic　benefits　and　the　environmental　burdens　from　carbon　emissions　was　analyzed　by　considering　the　effect　of　a　carbon　tax　scheme　on　the　reverse　logistics　network　design.　Through　an　improved　and　modified　interval　linear　programming　method,　the　optimal　interval　solution　was　obtained　with　LINGO.　Finally,　numerical　simulations　were　conducted　to　explore　the　effectiveness　of　the　model　and　the　effect　of　the　carbon　tax　scheme.　Results　show　that　the　optimal　solution　of　the　reverse　logistics　network　design　is　robust.　The　effect　of　the　carbon　tax　scheme　is　trivial　when　the　carbon　tax　is　low　and　significant　when　the　carbon　tax　is　high.　As　carbon　tax　gradually　increases,　carbon　emissions　effectively　decrease,　but　sharply　declines　the　total　profit　sharply　declines.　The　findings　indicate　that　the　proposed　model　can　effectively　solve　the　reverse　logistics　network　design　with　partial　information　under　a　carbon　tax　scheme.　©　2016　Eastern　Macedonia　and　Thrace　Institute　of　Technology.