Efficiency assessment of two-stage systems with fixed-sum outputs: A noncooperative DEA model with uncertain stage priority

Exogenous constraints such as fixed-sum output can affect the efficiency assessment of traditional two-stage data envelopment analysis (DEA) models. To address this issue, several studies have evaluated the DEA efficiencies for two-stage systems with fixed-sum output. They have proposed centralized models based on cooperative game theory and models under global mindset. However, in many cases, the first and second stages play a noncooperative game, and information on stage priority is often unobservable. In this study, we develop a noncooperative two-stage fixed-sum output DEA model with uncertain stage priority for calculating the overall system and stage efficiencies. Instead of stage priority as an endogenous variable, with aid of acceptaiblty analysis, we analyze the dominance relationship among decision-making units (DMUs) and provide a robust ranking by considering all possible stage priorities. We also conduct an empirical analysis with data from commercial banks to demonstrate the effectiveness of the developed model. After 10,000 groups of stage priority iterations, we report a robust ranking of commercial banks in which Hefei branch ranks first with 100 % probability.