The　paper　studies　a　two-machine　flowshop　with　unavailability　interval　on　the　second　machine.　Contrary　to　most　literature　where　machines　are　available　at　all　times,　this　means　that　the　machine　may　not　always　be　available　during　the　scheduling　period,　it　needs　a　constant　time　to　maintain　the　machine　after　completing　a　fixed　number　of　jobs　at　most.　The　objective　is　to　find　the　optimal　job　schedule　such　that　the　makespan　is　minimized.　We　focus　on　the　relationship　between　the　solution　and　the　Johnson　rule,　and　the　performance　of　the　Johnson　rule　as　a　heuristic　when　the　job　is　resumable,　analysis　the　worse-case　performance　ratio　of　the　Johnson　rule　as　a　heuristic.　Demonstrate　the　complexity　of　the　problem　when　the　job　is　nonresumable.　©　2015　IEEE.