Scheduling production optimally in multistage multiproduct plants with nonidentical parallel units is a very difficult but routine problem that has received limited attention. In this paper, we construct, analyze, and rigorously compare a variety of novel mixed-integer linear programming formulations using unit-slots, stage-slots, process-slots, a variety of slot arrangements and sequence-modeling techniques, 4-index and 3-index binary variables, etc. While two of our 4-index models are an order of magnitude faster than existing models on 22 test problems of varying sizes, we find that no single model performs consistently the best for all problems. Our work suggests that the best strategy for solving difficult scheduling problems may be to use a set of competitive models in parallel and terminate them all, when one of them achieves the desired solution. We also develop several heuristic models based on our formulations and find that even a heuristic based on an inferior model can surpass others based on superior models. Thus, it may not always be wise to just aim for a single best model for a given scheduling problem, but a host of novel and competitive models, as we have done in this paper. (c) 2006 Elsevier Ltd. All rights reserved.