Title: Benchmarking decision-making units' efficiency for the case of integer-valued data and fixed factors: a super efficiency slacks-based measure approach

Authors: Mushtaq Taleb; Mamdooh AttAllah; Ruzelan Khalid; Rosshairy Abd Rahman

Addresses: College of Administration and Economics, University of Anbar, Ramadi, Iraq ' College of Administration and Economics, University of Anbar, Ramadi, Iraq ' School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, 06010 UUM Sintok, Malaysia ' School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, 06010 UUM Sintok, Malaysia

Abstract: The purpose of this paper is to develop a mixed integer super efficiency slacks-based measure (SE-SBM) approach with fixed inputs and outputs. The proposed approach is developed by modelling the integer requirements and fixed inputs and outputs into the objective function and the input and output constraints of Tone's (2002) SE-SBM approach in data envelopment analysis (DEA). The scalar measure of the proposed approach depends on the discretionary mixed integer input excesses and discretionary mixed integer output shortfalls, as well as discretionary mixed integer input savings and discretionary mixed integer output surpluses. The approach can also identify sources of super-efficient status of efficient banks by identifying their discretionary mixed integer inputs that can be increased and/or discretionary mixed integer outputs that can be decreased. The proposed approach guarantees the feasibility condition under the variable returns-to-scale and constant returns-to-scale technologies. A banking sector application of the proposed approach with four inputs and four outputs is run.

Keywords: integer DEA; fixed factors; slacks-based measure; super efficiency; banking sector.

DOI: 10.1504/IJMOR.2026.152957

International Journal of Mathematics in Operational Research, 2026 Vol.33 No.4, pp.501 - 545

Received: 12 Sep 2023
Accepted: 22 Dec 2023
Published online: 17 Apr 2026 *

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