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?

Abstract: 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.