Scheduling problems often involve multiple conflicting objectives, requiring robust optimization strategies. This study presents an optimization framework for single-machine scheduling that simultaneously addresses two key performance measures: total earliness (∑E_j) and maximum lateness (L_max). The framework is designed to handle both problems with separate criteria and problems combining these objectives into a single evaluation, integrating exact methods including the Complete Enumeration Method (CEM) and Branch and Bound (BAB) alongside heuristics such as MST-EDD and Dominance Rule. Computational experiments on problem instances ranging from 3 to 4500 jobs provide insights into algorithm performance. CEM efficiently solves instances up to 11 jobs, while BAB handles up to 35 jobs. For larger instances, heuristic methods perform better, with MST-EDD outperforming the Dominance Rule. These results demonstrate the effectiveness of the proposed framework in optimizing multiple objectives simultaneously, providing valuable insights for complex single-machine scheduling scenarios.