Gas turbine engines (GTEs) are widely used for power generation, ranging from stationary power plants to airplane propulsion systems. Compressor fouling is the dominant degradation mode in gas turbines that leads to economic losses due to power deficit and extra fuel consumption. Washing of the compressor removes the fouling matter and retrieves the performance, while causing a variety of costs including loss of production during service time. In this paper, the effect of fouling and washing on the revenue of the power plant is studied, and a general solution for the optimum time between washes of the compressor under variable fouling rates and demand power is presented and analyzed. The framework calculates the savings achievable with optimization of time between washes during a service period. The methodology is utilized to optimize total costs of fouling and washing and analyze the effects and sensitivities to different technical and economic factors. As a case study, it is applied to a sample set of cumulative gas turbine operating data for a time-between-overhauls and the potential saving has been estimated. The results show considerable saving potential through optimization of time between washes.