The　performances　of　decision-making　units　(DMUs)　can　be　measured　from　two　different　points　of　view:　optimistic　or　pessimistic,　which　leads　to　two　different　efficiencies　for　each　DMU:　the　best　relative　efficiency　and　the　worst　relative　efficiency.　The　conventional　data　envelopment　analysis　(DEA)　considers　only　the　best　relative　efficiency.　It　is　argued　that　the　two　different　efficiencies　should　be　considered　together　and　any　approach　considers　only　one　of　them　is　biased.　This　paper　proposes　to　integrate　the　two　different　efficiencies　into　a　geometric　average　efficiency,　which　measures　the　overall　performance　of　each　DMU.　It　is　found　that　the　geometric　average　efficiency　has　better　discriminating　power　than　either　of　the　two　efficiencies.　This　is　illustrated　by　two　numerical　examples.　©　2007　Operational　Research　Society　Ltd.　All　rights　reserved.