The　conventional　BCC　model　is　based　on　a　fixed　production　possibility　set.　As　the　input–output　data　gathered　from　real　production　systems　may　be　expressed　by　interval　numbers,　the　production　possibility　sets　are　variable　within　a　certain　range.　To　enrich　the　interval　BCC　models,　two　parameter　vectors　were　introduced　to　represent　the　variabilities　of　the　production　possibility　sets.　The　necessary　and　sufficient　conditions　for　the　DMUs　to　reach　Pareto　efficiency　under　the　variable　production　possibility　sets　were　shown　and　expanded　production　efficiency　frontiers　were　formulated.　Then,　the　inclusion　relationship　between　different　frontiers　were　expressed,　and　their　convexities　were　discussed.　Furthermore,　RTS　classifications　of　the　arbitrary　inner　points　of　DMUs　were　decided　according　to　the　optimal　production　efficiency　frontier　and　were　proposed　for　technical　efficient　DMUs.　An　example　of　an　interval　number　was　introduced　to　show　the　rationality　and　validity　of　the　method.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH,　DE　part　of　Springer　Nature.