Scheduling problems are central to operations research because of their direct impact on productivity, resource utilization, and system responsiveness. This study addresses a novel tri-criteria and tri-objective model that provides an innovative framework for analyzing complex single-machine scheduling problems of minimizing total completion time (∑ ), total earliness (∑ ), and maximum lateness ( ), as well as their aggregated form. The problem remains computationally challenging for large job sizes (up to n = 8000). To evaluate solution performance, three independent approaches were employed: the Branch and Bound (BAB) algorithm and two local search methods, Tabu Search and the Bees Algorithm. While BAB provides precise answers for small cases (n ≤ 19) with low AAE, its computational time increases significantly with problem size. Tabu Search balances solution quality and computational effort to produce near-optimal solutions with modest execution times for medium and large-scale examples (n = 500–8000). While the Bees Algorithm may not match the precision of exact approaches, it offers faster computation and produces a variety of solution patterns. These features make it especially appropriate for large-scale problems or situations with restricted computational time. Moreover, this study offers practical insights to support the selection of suitable solution techniques, taking into account problem size, available computational resources, and the required balance between efficiency and solution quality.