In　this　paper,　most　productive　scale　size　(MPSS)　for　input　and　output　mixes　is　measured　from　pessimistic　point　of　view　by　using　pessimistic　data　envelopment　analysis　(DEA).　It　is　proved　that　the　decision　making　unit　(DMU)　with　the　maximum　pessimistic　efficiency　represents　MPSS.　However,　the　optimistic　and　the　pessimistic　measurements　may　identify　different　DMU　as　MPSS.　To　find　the　optimal　DMU　that　represents　MPSS,　a　double　frontiers　approach　is　developed　by　using　the　Hurwicz　criterion　to　integrate　both　the　information　on　the　optimistic　and　the　pessimistic　frontiers.　Numerical　examples　are　provided　to　show　the　applications　of　the　proposed　methods　in　estimating　MPSS.　(C)　2013　Elsevier　B.V.　All　rights　reserved.