We propose two novel discrete-time mixed-integer programming models for simultaneous batching and scheduling in multipurpose batch plants with storage constraints. The proposed models adopt two different modeling approaches. The first is based on explicit labeling of batches, while the second is based on identifying possible batch size intervals for each order and the corresponding unit routings. We also present extensions that allow us to consider limited shared utilities (with both fixed and time-varying availability and cost), storage with capacity limits and stage-dependent batch sizes. Finally, we study how instance characteristics (e.g. expected number of batches per order, uniformity in unit capacities) impact the effectiveness of the proposed models. We show that by carefully selecting the model allows us to effectively solve large-scale instances. (C) 2017 Elsevier Ltd. All rights reserved.