A Hybrid Approach Based on a Cross-Efficiency Model to Measure the Efficiency of Bank Currency Units in a Competitive-Cooperative Environment

This study aims to evaluate and rank the performance of the currency units of the bank by using the integrated methods of the balanced scorecard, cross-efficiency data envelopment analysis, and game theory in a cooperative-competitive environment. In this regard, by studying the indices used to evaluate the efficacy of banks and with the help of experts in foreign exchange, seven indices are selected as inputs and outputs from four perspectives of the balanced scorecard approach. Then, by applying the proposed Nash bargaining game model in cross-efficiency in a competitive-cooperative environment, the efficiency of decision-making units is evaluated. In this way, the bank’s branches compete in pairs. As a result, each branch tends to prioritize the other branch over the criteria in which they have a more significant advantage and allocate higher weight. This leads to the higher efficiency of the branch. Thus, the cross-performance matrix is ​​complemented by the performance of the bargaining model, rather than being filled by the performance of the conventional data envelopment analysis model. The proposed approach presents a new aspect of measuring performance based on the cross-efficiency model. The real case study of Isfahan Bank Melli branches is used to show the process of implementation of the model as well as the ability of the proposed approach.