It　has　been　widely　recognized　that　data　envelopment　analysis　(DEA)　lacks　discrimination　power　to　distinguish　between　DEA　efficient　units.　This　paper　proposes　a　new　methodology　for　ranking　decision　making　units　(DMUs).　The　new　methodology　ranks　DMUs　by　imposing　an　appropriate　minimum　weight　restriction　on　all　inputs　and　outputs,　which　is　decided　by　a　decision　maker　(DM)　or　an　assessor　in　terms　of　the　solutions　to　a　series　of　linear　programming　(LP)　models　that　are　specially　constructed　to　determine　a　maximin　weight　for　each　DEA　efficient　unit.　The　DM　can　decide　how　many　DMUs　to　be　retained　as　DEA　efficient　in　final　efficiency　ranking　according　to　the　requirement　of　real　applications,　which　provides　flexibility　for　DEA　ranking.　Three　numerical　examples　are　investigated　using　the　proposed　ranking　methodology　to　illustrate　its　power　in　discriminating　between　DMUs,　particularly　DEA　efficient　units.　©　2008　Elsevier　B.V.　All　rights　reserved.