Efficiency evaluation for decision making units with fixed-sum outputs using data envelopment analysis and stochastic multicriteria acceptability analysis

The generalized equilibrium efficient frontier data envelopment analysis (GEEFDEA) approach, an extension of the DEA method, has been widely used to solve the problem of evaluating decision making units (DMUs) producing fixed-sum outputs. It constructs a common equilibrium efficient frontier through a minimum reduction strategy for fixed-sum outputs and uses this frontier as a benchmark to achieve a complete ranking of DMUs. However, the existence of multiple feasible equilibrium efficient frontiers may lead to inconsistency in the evaluation criteria, and this possibility limits the method's usefulness. In this paper, an integrated framework for solving this problem is proposed to rank DMUs by using stochastic multicriteria acceptability analysis (SMAA-2) method combined with the GEEFDEA approach. Instead of using a certain common equilibrium efficient frontier as in conventional GEEFDEA approaches, we explore all possible frontiers to answer various robustness questions by computing rank acceptability indices and pairwise winning indices. Furthermore, we derive the complete ranking from the dominance relationships among the DMUs. Two numerical examples are used to demonstrate the effectiveness and rationality of the proposed hybrid approach.