While　single-period　stochastic　inventory　problems　have　been　studied　in　academia　and　industry,　the　impacts　of　both　carbon　emissions　reduction　and　partial　distribution　information　have　not　been　investigated.　In　this　paper,　we　consider　carbon　emission　reduction　in　a　single-period　inventory　problem　where　both　product　price　and　demand　are　stochastic.　When　only　partial　information　on　the　first　and　second　moments　of　the　two　stochastic　elements　is　specified,　we　use　the　max-min　criterion　to　construct　two　optimization　models　under　cap-and-trade　and　carbon　tax　policies.　For　each　model,　we　prove　the　existence　of　the　optimal　robust　decisions　on　production　quantity　and　cleaning　equipment　investment.　By　comparing　the　profit　and　carbon　emission　between　these　two　models,　we　identify　certain　conditions　that　improve　the　economic　and　environmental　performance　of　the　manufacturer.　Finally,　we　conduct　a　numerical　study　to　test　the　robustness　of　the　optimal　operational　decisions　under　each　carbon　policy.