A new two-stage Stackelberg fuzzy data envelopment analysis model

Data Envelopment Analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of Decision Making Units (DMUs). Conventional DEA methods treat DMUs as “black boxes”, focusing entirely on their relative efficiencies. We propose an efficient two-stage fuzzy DEA model to calculate the efficiency scores for a DMU and its sub-DMUs. We use the Stackelberg (leader–follower) game theory approach to prioritize and sequentially decompose the efficiency score of the DMU into a set of efficiency scores for its sub-DMUs. The proposed models are linear and independent of the α-cut variables. The linear feature allows for a quick identification of the global optimum solution and the α-cut independency feature allows for a significant reduction in the computational efforts. Monte Carlo simulation is used to discriminately rank the efficiencies in the proposed method. We also present a case study to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed method to a two-stage performance evaluation problem in the banking industry.