We　study　the　problem　of　two-machine　no-wait　flowshop　scheduling　with　learning　effect　and　convex　resource-dependent　processing　times.　Under　the　condition　of　the　due-date　assignment　with　common　flow　allowance　(i.e.　slack　(SLK)　due-date　assignment),　we　provide　a　bi-criteria　analysis　where　the　first　criterion　is　to　minimise　the　scheduling　criteria　(i.e.　the　weighted　sum　of　earliness,　tardiness　and　flow　allowance　costs),　and　the　second　criterion　is　to　minimise　the　resource　consumption　cost　(i.e.　the　weighted　sum　of　resource　consumption　cost).　The　objective　is　to　determine　the　optimal　job　sequence,　resource　allocations　and　common　(flow　allowance)　slack　time　that　minimise　the　three　different　versions　of　the　two　criteria.　We　prove　that　these　problems　can　be　solved　in　polynomial　time.　©　2018,　©　2018　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.