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This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships between constraints that allow relaxing some decision variables. The second approach (ODH) is based on linear ordering and disjunctive formulations. In this work, we prove ODH to be the most efficient formulation known so far. The experiments have been carried out with a large set of problems, which consider single machines and identical parallel machines. Computational results show that OPH is better than the rest of the existing formulations for the case of weighted completion objectives, while ODH turns out to be the best approach for most scenarios studied.