This paper presents a novel approach to solve the Close Enough Traveling Salesman Problem (CETSP). It aims to simplify the mathematical formulation by approximating the Euclidean distance and restructuring the objective function. It also provides computational advantages by using convex sets for constraint design. The proposed methodology is experimentally verified on real CETSP instances by utilizing computational strategies such as partitioned CPLEX-based approaches. The results demonstrate the effectiveness of efficiently managing computational resources without compromising the quality of the solution. Furthermore, the behavior of the proposed mathematical formulation is analyzed to provide comprehensive insights into its performance.