Inverse　data　envelopment　analysis　(DEA)　method　is　a　useful　tool　for　analyzing　the　optimization　of　resource　allocation　of　a　set　of　homogeneous　decision-making　units　(DMUs).　However,　the　assumption　of　homogeneity　for　DMUs　is　not　necessarily　applied　in　reality.　For　example,　universities　with　the　same　input　structure　cultivate　students　with　different　orientations;　power　plants　consume　different　resources　to　generate　electricity.　Therefore,　how　to　handle　nonhomogeneous　DMUs　in　inverse　DEA　becomes　an　issue　when　analyzing　the　optimization　of　resource　allocation.　In　this　study,　an　inverse　DEA　method　for　nonhomogeneous　DMUs　under　constant　returns　to　scale　(CRS)　is　proposed　to　handle　the　aforementioned　issue.　Furthermore,　the　inverse　DEA　method　for　nonhomogeneous　DMUs　is　extended　to　the　case　of　variable　returns　to　scale　(VRS).　The　adjustment　range　of　inputs-outputs　under　VRS　is　discussed　to　avoid　the　problem　of　infeasibility,　and　relevant　properties　of　our　method　are　proved.　Moreover,　the　effect　of　frontier　changes　on　the　proposed　method　is　also　discussed.　Finally,　numerical　examples　are　provided　to　illustrate　the　effectiveness　of　our　method.　©　Operational　Research　Society　2024.