The use of Data-Envelopment Analysis (DEA) to determine the most efficient Decision Making Unit (DMU) has drawn attention in the literature. For some applications of DEA, decision-makers may only want to identify the most efficient DMU rather than determining the efficiencies of all possible DMUs. In this study, we present an modified model based on model in Özsoy et al. [1], A simplistic approach without epsilon to choose the most efficient unit in DEA. Expert systems with applications, 2021. 168: p. 114472] to identify the most efficient DMU. The proposed model with low complexity respect to model in [1] find only one DMU with an efficiency score greater than one, while all others receive scores strictly less than one. This structure enhances the model’s ability to fully rank all units. To demonstrate its effectiveness and compare it with two well-known models, the proposed model is applied to two real-world examples from the literature. The results show the appropriate performance of the proposed model in identifying the most efficient units and full ranking of the units.