Along　with　developing　of　the　technology　of　Grid　workflows　and　Cloud　workflows,　recent　researches　into　the　problem　of　scheduling　multiple　DAG　(Directed　Acyclic　Graph)　sharing　resources　have　been　making　progress　and　have　solved　some　problems.　However,　the　problems　of　scheduling　and　cost　optimization　of　multiple　DAGs　with　deadline　sharing　finite　heterogeneous　resources　need　to　be　solved.　To　solve　the　problems,　a　new　method　of　＇relative　strictness＇　used　in　measuring　urgency　level　of　a　DAG＇s　deadline　constraint　is　proposed　first,　and　then,　the　MDRS　algorithm　is　presented.　The　algorithm　can　not　only　reasonably　determine　the　relationship　of　multiple　DAGs＇　urgency　levels,　but　also　can　deal　with　possible　＇oversaturation＇　which　may　be　caused　by　rigid　deadline　constraints　of　each　DAG.　Once　the　＇oversaturation＇　happens,　the　algorithm　can　drop　as　few　DAGs　as　possible　and　try　to　schedule　the　rest　of　DAGs　to　maximize　the　throughput　of　DAG　through　the　mechanism　of　＇Backtracking＇　combining　with　＇Stack＇.　Furthermore,　in　order　to　fairly　minimize　the　total　cost　of　these　DAG　while　meeting　a　user-defined　deadline,　we　propose　another　algorithm　called　CDVRS　(Cost　Decrease　based　on　Variance　of　the　Relative　Strictness).　Last　experiments　demonstrate　that　our　algorithms　and　methods　can　improve　the　related　performances.