This paper presents two new multiple-time grid, continuous-time mixed integer linear program (MILP) models for the short-term scheduling of multistage, multiproduct plants featuring equipment units with sequence dependent changeovers. Their main difference results from the explicit consideration of changeover tasks as model variables rather than implicitly through model constraints. The former approach is more versatile in terms of type of objective function that can be efficiently handled (minimization of total cost, total earliness, and makespan), and despite generating larger mathematical problems, it is also a better performer in single stage problems. The latter is better suited for multistage problems, where the former approach has some difficulties even in finding feasible solutions, particularly as the number of stages increases. The performance of both formulations is compared to other MILP and constraint programming models. The results show that multiple-time grid models are better suited for single stage problems or, when minimizing total earliness, that the constraint programming model is the best approach for makespan minimization and that the continuous-time model with global precedence variables is the best overall performer.