A　neutral　data　envelopment　analysis　(DEA)　model　for　cross-efficiency　evaluation　was　recently　proposed　by　Wang　and　Chin　[Wang　and　Chin　(2010b).　A　neutral　DEA　model　for　cross-efficiency　evaluation　and　its　extension.　Expert　Systems　with　Applications,　37(5),　3666-3675],　which　maximinimizes　the　relative　efficiency　of　each　output　and　effectively　reduces　the　number　of　zero　weights　of　outputs.　Since　a　large　number　of　zero　weights　may　still　exist　among　inputs,　this　paper　proposes　a　simultaneously　input-　and　output-oriented　weight　determination　DEA　model　for　the　cross-efficiency　evaluation.　The　new　DEA　model　proves　to　reduce　the　number　of　zero　weights　for　both　inputs　and　outputs　very　significantly,　as　illustrated　by　numerical　examples.　The　weights　determined　by　the　new　DEA　model　are　neutral,　neither　aggressive　nor　benevolent.　(C)　2011　Elsevier　Ltd.　All　rights　reserved.