This paper deals with a sustainable personnel scheduling problem of personnel working in a large-scale natural gas combined-cycle power plant in Turkey. The proposed model focuses on employee complaints due to unfair work schedules and the results of balanced assignments based on power plant interruptions. Eighty personnel work in three shifts at this natural gas combined-cycle power plant. The model is solved with respect to some of the workers’ skills, and there are 20 criteria regarding skills. The analytic network process method is used to get the weights of workers’ skills, which are calculated and included in the model. Goal programming is used in this paper. Our proposed model gives cost minimization and fair work schedules for the power plant. Compared with the literature, the number and set of criteria are unique in terms of personnel competency in the energy sector. Minimizing cost and imbalanced assignments was achieved by the proposed model for the first time without considering the sector.