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The empirical study consists of two parts. In the first part the relative efficiency of the branches of one of the leading Macedonian banks is measured by using the non-parametric approach Data Envelopment Analysis (DEA). In the second part a ranking of the city-branches of the bank is performed by using the multi-criteria decision making (MCDM) method Analytic Hierarchy Process (AHP). The developed models are solved by software tools, and the results obtained are analyzed and interpreted in a simple manner so as to be understood by non-experts in mathematics. The results give especially valuable information for the management of the bank (the relatively efficient and inefficient branches are identified, the trend can be observed, the ranking of the city-branches is presented, and by performing a sensitive analysis, it is determined that the ranking is stable). In the models that have been developed, the knowledge of the respondents who are experts in banking is incorporated, thus contributing to the study being successful. The obtained results were presented and interpreted in the bank and they correspond to the actual situation and perceptions of the management.