Abstract
Evaluating the performance of banks is important to governments and bankers, but it is also important to investors. Usually, retail investors judge the strength of a bank by its return on capital ratio. However, that ratio does not fully assess how efficiently the inputs are used to produce the outputs. In this paper, we examine different methods to evaluate the efficiency of Vietnam's commercial banks. Three problems A, B, and C are proposed to measure efficiency. A Decision-Making Unit that is A-efficient is not necessarily B-efficient; similarly, a Decision-Making Unit that is B-efficient may not necessarily be C-efficient. Conversely, if a Decision-Making Unit is C-efficient, then it is certainly B-efficient and A-efficient. We have proven the existence of solutions to the problems and run experiments for 26 commercial banks in Vietnam. The obtained results prove the theory's correctness and measure banks' relative efficiency.