Interval cross-EEF evaluation approach for ranking DMUs with fixed sum outputs: A vehicle industry application

Fixed-sum output data envelopment analysis (DEA) models are extensions of DEA and have been widely used to measure the performance of decision-making units (DMUs) with fixed-sum outputs. Considering the opinions of other DMUs, a cross-equilibrium efficient frontier (EEF) efficiency method was proposed to rank DMUs, where each DMU can choose a favorable EEF to evaluate itself and the others. However, in some cases, the favorable EEFs of the DMUs are multiple. Multiple EEFs produce multiple cross-EEF efficiencies. To eliminate this flaw, this study proposes an interval cross-EEF evaluation model that allows DMUs to select all favorable EEFs to evaluate themselves and others. All DMUs with interval cross-EEF efficiencies can be fully ranked by applying the stochastic multi-criteria acceptability analysis approach. Finally, we demonstrate the effectiveness and feasibility of the proposed method using a dataset of 32 companies in the vehicle industry for the year 2022.