This study develops a Hybrid Systems DEA model to analyze the influence of automatic service on bank performance. There are two assumptions seldom used in prior banking studies that are introduced into the DEA model. The first assumes that automatic service inputs do not change proportionally with branch service inputs. The second assumes banks that employ different operating types have different frontier technologies. The inefficiency sourced from excess inputs in automatic and branch service is evaluated through the empirical model. Results show that the excess input in automatic service is the cause of lower efficiency in financial holding banks when compared to independent banks. On the other hand, increasing inputs in automatic services do not result in a negative impact on independent banks. The finding also indicates that the cross-learning initiatives between the two groups is effective in reducing the inefficiency caused from excess automatic service but ineffective for excess branch service.

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The purpose of this note is to add some important properties to the results obtained in [2]. Specifically, it is shown that (i) an apportionment for relaxed divisor methods remains unchanged over an interval and (ii) any relaxed divisor method approaches the Webster method as the house size increases.

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In this work, a version of the technique for order preference by similarity ideal solution (TOPSIS) with entropic regularization approach is developed for solving the fuzzy multi-objective nonlinear programming (MONLP) problems. Applying the basic principle of compromise of TOPSIS, the fuzzy MONLP problem can be reduced into a fuzzy bi-objective nonlinear programming problem. Moreover, following the "tolerance approach," the solution of the fuzzy bi-objective nonlinear programming problem can be obtained by solving a min-max problem. An entropic regularization approach is then applied for solving such a problem. Computational results are provided to illustrate the validity and efficiency of the proposed method.

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