Developing and Presenting a Fixed-Cost Allocation Scheme for Commercial Banks Based on Data Envelopment Analysis in the Presence of Undesirable Outputs

Abstract

Objective: This study aimed to develop and present a generalizable fixed-cost allocation scheme for commercial banks based on Data Envelopment Analysis while simultaneously incorporating desirable and undesirable outputs.

Methodology: This developmental and applied study employed a descriptive-survey and cross-sectional design. The study population consisted of Iranian commercial banks, and the empirical application included 14 banks observed over two consecutive years, yielding 28 bank-year observations. The model inputs were personnel expenses, net interest expenses, and non-interest expenses, while the desirable outputs comprised net interest income, non-interest income, and total deposits. Overdue claims were incorporated as the undesirable output. A DEA-based fixed-cost allocation model was developed, and three allocation strategies were compared: equal allocation, scale-based allocation, and the proposed allocation scheme. The mathematical models and sensitivity analyses were implemented using GAMS and Python, while complementary analyses were conducted in SPSS.

Findings: The baseline mean efficiency score before fixed-cost allocation was 0.956, with 42.86% of observations located on the efficiency frontier. Under equal allocation, mean efficiency increased to 0.962 and the proportion of efficient observations rose to 53.57%. Scale-based allocation increased mean efficiency to 0.981, with 67.86% of observations becoming efficient. The best performance was obtained under the proposed scheme, assigning a weight of 0.95 to operating scale and 0.05 to the undesirable output. Under this specification, mean efficiency increased to 0.983 and 71.43% of the observations reached the efficiency frontier. Sensitivity analysis showed that increasing the undesirable-output weight above 0.05 progressively reduced both average and minimum efficiency.

Conclusion: The findings indicate that combining operating scale with a limited adjustment for overdue claims provides a more efficient and balanced fixed-cost allocation mechanism than equal or purely scale-based allocation and better reflects efficiency, credit quality, and allocation fairness in commercial banks.