We　consider　an　assembling　manufacture　system　where　several　suppliers　provide　component　parts　to　a　manufacturer,　who　assembles　products　from　all　the　supplied　component　parts.　The　delivery　time　of　any　product　is　the　maximum　of　the　suppliers＇　delivery　time　of　the　parts　needed　for　that　product.　We　assume　that　the　final　stage　is　non-bottleneck.　Chen　and　Hall　(2007)　show　that　the　suppliers＇　problem　of　minimizing　the　total　weighted　number　of　tardy　parts　is　binary　(i.e.,　weakly)　NP-hard　and　left　open　whether　it　is　unary　(i.e.,　strongly)　NP-hard.　In　this　paper　we　resolve　this　open　problem　by　showing　that　it　is　unary　NP-hard.　Moreover　we　show　that　the　suppliers＇　problem　of　minimizing　the　total　late　work　of　parts　is　also　unary　NP-hard.　(C)　2013　Elsevier　B.V.　All　rights　reserved.