This paper proposes a methodology that improves the performance of uniform time grid, continuous-time scheduling formulations, in problems involving changeovers. The procedure consists of dividing the problem into complementary subproblems of lower complexity based on simple structural decisions and subsequently solving all of the subproblems. The performance of the proposed strategy is illustrated through the solution of three example problems that have been thoroughly examined in the literature, two concerning short-term scheduling problems and one concerning a periodic scheduling problem. The results show that it is best, to solve several subproblems sequentially rather than one single large problem. Moreover, in the case of the nonconvex periodic scheduling problem, the proposed methodology was able to generate substructures that guided the solver to closer-to-the-global-optimum regions of the search space. For this specific example, the use of a general continuous-time formulation together with the proposed methodology leads to a solution that is 18.8% better than the best solution reported in the literature.