Goal: Hydrogen has shown increasing demand in oil refineries, due to the importance of its use as a sulfur capture element. As different oils and products require different amounts of hydrogen, their use optimally is an essential tool for refinery production scheduling. A comparison was made between the different approaches used in optimization via mathematical programming. Design / Methodology / Approach: One of the most used methods for hydrogen network optimization is through mathematical programming. Linear and non-linear models are discussed, positive aspects of each formulation and different initialization techniques for non-linear modeling were considered. Results: The optimization through the linear model was more satisfactory, taking into account the payback of the new proposed design, combined with the use of compressor rearrangement, which reduces the investment cost. Limitations of the investigation: The objective function chosen is based on the operational cost, but another approach to be considered would be the total annual cost. In addition, the parameters related to costs are obtained from the literature and may change over the years. Practical implications: The proposal is to discuss the main aspects of each model, showing which models more robust and easier to converge are capable of providing competitive results. Also, different initialization techniques that can be used in future works. Originality / Value: The main contribution is the relationship between hydrogen management and production scheduling and for that, a discussion is made about possible formulations. Linear model is sufficient to optimize the problem, due to its main characteristics discussed.