In response to the global shift towards renewable energy resources, the production of green hydrogen through electrolysis is emerging as a promising solution. Modular electrolysis plants, designed for flexibility and scalability, offer a dynamic response to the increasing demand for hydrogen while accommodating the fluctuations inherent in renewable energy sources. However, optimizing their operation is challenging, especially when a large number of electrolysis modules needs to be coordinated, each with potentially different characteristics. To address these challenges, this paper presents a decentralized scheduling model to optimize the operation of modular electrolysis plants using the Alternating Direction Method of Multipliers. The model aims to balance hydrogen production with fluctuating demand, to minimize the marginal Levelized Cost of Hydrogen (mLCOH), and to ensure adaptability to operational disturbances. A case study validates the accuracy of the model in calculating mLCOH values under nominal load conditions and demonstrates its responsiveness to dynamic changes, such as electrolyzer module malfunctions and scale-up scenarios.