In　recent　times,　there　has　been　a　growing　momentum　towards　green　manufacturing　in　the　production　industry,　with　low-carbon　manufacturing　emerging　as　an　essential　component　of　this　eco-friendly　approach.　Numerous　factories　face　challenges　in　transitioning　to　greener　equipment　and　low-carbon　technologies　due　to　constraints　such　as　limited　technological　capabilities,　insufficient　investments,　outdated　management　practices,　and　inadequate　human　resources.　Among　various　solutions,　optimizing　job　shop　management　stands　out,　offering　a　pathway　that　requires　less　investment,　lower　risk,　and　lower　uncertainty　with　an　enhanced　adaptability.　This　study　presents　an　innovative　approach　for　factories　to　reduce　carbon　emissions　without　compromising　production　efficiency.　This　paves　the　way　for　factories　to　achieve　green　manufacturing　and　carbon　neutrality.　First,　we　establish　a　low-carbon　FJSP　(Flexible　Job-Shop　Scheduling　Problem)　mathematical　model.　Then,　we　employ　the　enhanced　Non-dominated　Sorting　Genetic　Algorithm　II　to　resolve　the　scheduling　problem　for　the　specific　factories.　With　enumerated　arithmetic,　we　finally　determine　the　weight　ratio　of　the　low-carbon　FJSP　model,　balancing　carbon　dioxide　reduction　and　productivity　maintenance.　Our　findings　indicate　that　the　integration　of　carbon　emissions　into　job　shop　scheduling　not　only　reduces　carbon　emissions,　but　also　ensures　sustained　productivity.　This　research　illustrates　that　the　reduction　of　carbon　emissions　does　not　necessarily　lead　to　the　decline　of　productivity　in　small,　medium,　and　large-scale　production.　It　provides　a　novel　perspective　for　factories　of　all　sizes　to　address　challenges　in　green　and　low-carbon　manufacturing.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG　2024.