Fixed cost allocation plan based on robust optimization in data envelopment analysis: a case study of the banking industry

This study aims to propose a fair fixed cost allocation scheme among a set of Decision-Making Units (DMUs), such as banks or factories, in an uncertain environment. The allocation is designed in a way that does not reduce the efficiency of the DMUs and may even lead to improvements in efficiency.

To achieve this goal, a model is developed based on Data Envelopment Analysis (DEA) integrated with robust optimization. Inputs and outputs of the DMUs are considered fuzzy random variables to reflect environmental uncertainty. The model is linearized and converted into a deterministic programming model using principles from stochastic programming. Furthermore, the concept of a common set of weights is utilized to ensure fairness in the allocation process.

The results indicate that, under the proposed fixed cost allocation plan, the efficiency scores of the DMUs (banks) are not only maintained but also improved in many cases. This confirms the effectiveness of the model in preserving and enhancing performance under uncertain conditions.

 The novelty of this research lies in the integration of DEA and robust optimization in uncertain environments to design a cost allocation model that ensures non-decreasing efficiency. The use of a common set of weights adds to the fairness of the approach. Additionally, applying the model to the Iranian banking sector highlights its practical relevance and managerial value.