This study conducts a rigorous comparative analysis of two prominent flow shop scheduling heuristics the Johnson’s Rule (JR) and the Time Deviation Rule (TDR) by validating their performance against an exact Branch and Bound (B&B) algorithm. The primary objective is to determine which heuristic provides solutions closest to the proven optimum for the key performance metrics of Total Elapsed Time (TET) and Total Idle Time (TIT). A computational experiment was designed using 15 benchmark problem instances of varying sizes and complexities. The exact B&B method was implemented to establish optimal solutions for each problem, serving as the validation benchmark. Both JR and TDR were applied to the same problem set. Performance was quantitatively evaluated by calculating the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) for each heuristic's TET and TIT results against the B&B-derived optimum. Data analysis and visualization were performed using MATLAB. The B&B algorithm consistently generated superior schedules, confirming its value as a benchmark. The error analysis revealed a nuanced performance trade-off between the heuristics. For minimizing TET, JR (MAE = 2.27) slightly outperformed TDR (MAE = 2.40). However, for minimizing TIT, TDR demonstrated a significant advantage, with both lower MAE (5.27 vs. JR's 6.53) and lower RMSE (9.49 vs. JR's 11.25). The aggregate results indicate that TDR provides a more robust and accurate overall approximation for sequencing problems. This research provides a critical, empirically-grounded validation of classical scheduling heuristics against an exact optimization method. It moves beyond simple TET comparison to offer a multi-metric evaluation, demonstrating that the TDR is generally a more reliable heuristic than JR for comprehensive schedule quality, particularly in optimizing machine utilization through idle time reduction. To enhance the generalizability of these findings, future work should involve larger-scale and real-world problem datasets. Furthermore, investigating the scalability of these methods and integrating them with metaheuristics in particular Genetic Algorithms and Simulated Annealing could yield even more powerful and efficient hybrid scheduling solutions.