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Decision-making units (DMUs) in a group convert the same resources (i.e.,input indices) into the same products (i.e., output indices) at differentscales. Performance indices have different measurement units, and their marketprices per unit are unobtainable. Data envelopment analysis (DEA) programsemploy linear programming to estimate the virtual weight and best slack ofevery input and output index for each DMU, named DMU-o, to obtain the minimumrelative inefficiency against the DMUs. DMU-o reduces each input's slack, thesurplus, and expands each output's slack, the shortage, to the benchmark. EachDEA program specifies an artificial goal weight for each performance index. Therelative inefficiencies in the primal and dual models are the sum of theweighted slacks and the virtual gap of the total virtual weighted inputs to theoutputs, respectively. DEA programs have failed the uncountable attempts toconceive the artificial goal weight equal to the estimated virtual weight foreach performance index; therefore, they have incomplete solutions that some ofthe slacks could not be aggregated into the efficiency score. Our new virtualgap analysis program assesses DMU-o comprehensively. The four-phase procedureensures DMU-o has the achievable best benchmarks for implementation and itscompatible best peers to learn. Each DMU is a point in the 2D geometricintuition of the virtual technology set in assessing DMU-o. The best peers andthe improved DMU-o are on the best efficiency boundary. Inefficient DMUs aresituated underneath the boundary.

Data envelopment analysis models or the virtual gap analysis model:  Which should be used for identifying the best benchmark for each unit in a  group?