Ranking DMUs by using interval efficiencies in data envelopment analysis

Efficiency is a relative measure that allows assessment across different ranges. Evaluating the performance of decision-making units (DMUs) from an optimistic perspective yields the best relative efficiency (optimistic efficiency), which establishes an efficiency frontier. Conversely, evaluating from a pessimistic perspective produces the worst relative efficiency (pessimistic efficiency) and creates an inefficiency frontier. This study examines the efficiency of DMUs in two scenarios and proposes models for adjustment coefficient. The pessimistic and optimistic efficiencies are adjusted to the lower and upper bounds of the DMUs based on the adjustment coefficient, enabling determination of efficiency intervals for all DMUs, as well as evaluation and ranking. A Hurwicz criterion-based approach is introduced and applied to compare and rank the interval efficiencies of DMUs. Two numerical examples are examined using the proposed DEA adjustment coefficient models to demonstrate its potential application and validity.