Alternative Secondary Goals in Multiplicative Two-Stage Data Envelopment Analysis

Data envelopment analysis (DEA) is a nonparametric method for evaluating the relative efficiency of a set of decision-making units (DMUs) with multiple inputs and outputs. As an extension of the DEA, a multiplicative two-stage DEA model has been widely used to measure the efficiencies of two-stage systems, where the first stage uses inputs to produce the outputs, and the second stage then uses the first-stage outputs as inputs to generate its own outputs. The main deficiency of the multiplicative two-stage DEA model is that the decomposition of the overall efficiency may not be unique because of the presence of alternate optima. To remove the problem of the flexible decomposition, in this paper, we maximize the sum of the two-stage efficiencies and simultaneously maximize the two-stage efficiencies as secondary goals in the multiplicative two-stage DEA model to select the decomposition of the overall efficiency from the flexible decompositions, respectively. The proposed models are applied to evaluate the performance of 10 branches of China Construction Bank, and the results are compared with the results of the existing models.