Hydrogen has the potential to revolutionize the energy industry due to its clean-burning and versatile properties. It is the most abundant element in the universe and can be produced through a variety of methods, including electrolysis. The widespread adoption of hydrogen faces various challenges, including the high cost of production; thus, it is important to optimise the production processes. This research focuses on development of models for hydrogen production optimisation based on various external factors and parameters. Models based on electricity prices are developed and compared between different market situations. To run hydrogen production more effectively, it is required to use renewable energy sources for the production process. Adding the solar power component to the economic evaluation model outcome is more positive. The Monte Carlo tree search (MCTS) algorithm is adapted to effectively control the electrolysis process. MCTS schedule optimization was performed for a 24 h time horizon applying two time-resolution settings—1 h and 15 min. The results demonstrate the potential of the MCTS algorithm for finding good schedules for water electrolyser devices by taking into account variable environmental factors. Whereas the MCTS with a 15 min resolution ensures mathematically better results, it requires more computational power to solve the decision tree.