Cost Malmquist Productivity Index for Bi-level Units: A Case Study from Bank

Subject Areas : International Journal of Industrial Mathematics

Mona Habibpoor ¹ , Mohammadreza Alirezaee ² , Jalil Rashidinia ³

1 - Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
2 - Department of mathematics, Iran university of science and technology
3 - Department of Mathematics,Islamic Azad University,Central Tehran Branch,Iran

Received: 2022-09-30 Accepted : 2024-05-18 Published : 2024-09-02

Keywords: Data envelopment analysis, Bi-level structure, Cost efficiency, Productivity, Cost Malmquist index.,

Abstract :

Traditional cost models ignore the internal structure of decision-making units (DMUs), so, may produce ambiguous outcomes and provide a biased assessment. In this paper, we evaluate the performance of the units by considering their internal structures. We proposed a new cost Malmquist index for measuring the cost productivity change of the units with bi-level structures. The bi-level structure is a special case of hierarchical structures with two levels, where the leader unit is positioned at the upper level and followers are located at the lower level. The overall system of bi-level units tries to use inputs and produce outputs in a cost-efficient way. However, each subunit performs according to its goals and limited resources. This research tries to develop a bi-level cost model that is suitable for measuring the cost efficiency of bi-level units. Based on this model, a new cost Malmquist index (CMI) is suggested to evaluate the productivity changes of bi-level units. This index presents a new aspect of CMI and provides the productivity changes of units by considering the impact of the leader's and the subunits' performance. In addition, similar to the traditional CMI, it decomposes into various components, such as cost efficiency changes and cost technological changes. The developed CMI is applied to a real-world case study to evaluate eight management regions which all together manage 198 branches. The results show that the proposed CMI provides a more meaningful evaluation of DMUs compared to the conventional CMI.