Determining the equilibrium efficient frontier by proportional frontier shifting for data envelopment analysis with fixed-sum outputs

The equilibrium efficient frontier data envelopment analysis (EEFDEA) has been extensively used to evaluate efficiencies of the decision-making units (DMUs) with fixed-sum outputs. This study develops a new EEFDEA approach based on a proportional frontier-shifting strategy. Our approach applies an iterative procedure to find the equilibrium efficient frontier (EEF). Each iteration uses a proportional frontier-shifting model to improve an inefficient DMU to the efficient frontier by increasing its fixed-sum outputs. Meanwhile, the DMUs on the efficient frontier decrease fixed-sum outputs proportionally to ensure the total fixed-sum outputs are unchanged. Our theoretical developments show that the proportional frontier-shifting strategy is feasible and can finally obtain a unique EEF. The new approach allows DMUs to use their preferred input and output weights when determining the EEF. This generates an EEF that better aligns with real-world practices and avoids the need to construct it as a single hyperplane, as required by conventional EEFDEA methods. It also avoids unfair adjustments in fixed-sum outputs among the DMUs and eliminates the problem of peculiar efficiency evaluation results (i.e., some DMUs obtain extremely high, or infinity, efficiencies). Finally, we apply our approach to a case study of Chinese vehicle industry companies to demonstrate its usefulness and compare it with the previous representative approach.