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

Weijiao Wang, Fei Xu, Junfei Chu, Yanhua Dong and Zhe Yuan

Omega, 2025, vol. 130, issue C

Abstract: 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.

Keywords: Data envelopment analysis; Fixed-sum outputs; Proportional frontier-shifting; Fairness; Unique equilibrium efficient frontier (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.omega.2024.103174

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