  Decision-making units (DMUs) in a group convert the same resources (i.e.,
input indices) into the same products (i.e., output indices) at different
scales. Performance indices have different measurement units, and their market
prices per unit are unobtainable. Data envelopment analysis (DEA) programs
employ linear programming to estimate the virtual weight and best slack of
every input and output index for each DMU, named DMU-o, to obtain the minimum
relative inefficiency against the DMUs. DMU-o reduces each input's slack, the
surplus, and expands each output's slack, the shortage, to the benchmark. Each
DEA program specifies an artificial goal weight for each performance index. The
relative inefficiencies in the primal and dual models are the sum of the
weighted slacks and the virtual gap of the total virtual weighted inputs to the
outputs, respectively. DEA programs have failed the uncountable attempts to
conceive the artificial goal weight equal to the estimated virtual weight for
each performance index; therefore, they have incomplete solutions that some of
the slacks could not be aggregated into the efficiency score. Our new virtual
gap analysis program assesses DMU-o comprehensively. The four-phase procedure
ensures DMU-o has the achievable best benchmarks for implementation and its
compatible best peers to learn. Each DMU is a point in the 2D geometric
intuition of the virtual technology set in assessing DMU-o. The best peers and
the improved DMU-o are on the best efficiency boundary. Inefficient DMUs are
situated underneath the boundary.
