This study examines the application of the Lagrange method and Particle Swarm Optimization (PSO) in solving the Economic Dispatch problem at the Tanjung Jati B Steam Power Plant (PLTU). The main objective is to compare the effectiveness of both methods in optimizing load distribution among generation units and to evaluate potential operational cost savings compared to actual operating conditions. The optimization model minimizes a quadratic generation cost function, subject to system load demand and the power output limits of each unit. Simulation data includes daily load distribution and fuel-related parameters such as calorific value and fuel price. The results show that the Lagrange method yields an average power output of 2,367 MW, equal to the real condition, while PSO produces 1,966 MW, which is 16.94% lower. In terms of cost savings, PSO achieves an average saving of IDR 938,501, while the Lagrange method and real operation yield average savings of IDR 1,078,064 and IDR 1,073,076 respectively. In percentage terms, Lagrange shows 12.95% higher savings than PSO and 0.46% higher than the actual condition. This study highlights the importance of integrating optimization methods in power plant operations to improve efficiency and reliability of electricity supply.