This paper proposes a mathematical model for the optimal operation of the fuel cycle of ITER. The developed model aims to minimize the tritium inventory in the fuel cycle by adopting a two-phased scheduling approach. To consider multiple equipment in the fuel cycle, the proposed solving algorithm is designed as sequential scheduling models: (Phase I) to minimize tritium inventory in the vacuum roughing system and (Phase II) to minimize tritium working inventory in the isotope separation system. The scheduling models are developed based on a state-task-network method. Given a required amount of tritium for fueling scenarios considering ramp-up, flat-top, and ramp-down, the proposed model provides the optimal operation plan for deuterium-tritium plasma operation including information on fueling rate, duration, and timing between each unit. Among six case studies, the noninductive tokamak operation mode with high tritium demands showed the highest tritium working inventory during one burn-and-dwell cycle.