Efficiency intervals, rank intervals and dominance relations of decision-making units with fixed-sum outputs

How to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs is a timely and challenging question in data envelopment analysis (DEA). Two major challenges are (1) how to determine a common equilibrium efficient frontier and (2) how to deal with multiple feasible equilibrium efficient frontiers. This paper first uses a simple dataset to illustrate the possibility of multiple equilibrium efficient frontiers and the corresponding major differences in the DMUs’ efficiencies and rankings resulting from these frontiers. We address these challenges by considering all feasible equilibrium efficient frontiers and develop several models to obtain the corresponding efficiency intervals, ranking intervals and dominance relations for the DMUs with fixed-sum outputs. We illustrate the proposed approach with two numerical examples and show that it gives more informative results than previous DEA approaches. For example, there are interesting dominance relations between DMUs under the fixed-sum outputs; yet these relations do not exist when there are no fixed-sum outputs. In addition, the efficiency ranges and ranking intervals can be narrowed by accounting for policy suggestions such as adjustment constraints of fixed-sum outputs for DMUs.