In this article we present a new approach, relying on mixed-integer linear programming (MILP) formulations, for the design of multi-product batch plants with continuous sizes for processing units and host selection. The main advantage of the proposed approach is its scalability, that allows us to solve, within reasonable precision requirements, realistic instances. Furthermore, we show that many other alternatives are either numerically unstable (for the problem sizes that we are interested in), unable to solve large instances, or much slower than the proposed method. We present extensive computational experiments, which show that we are able to solve almost all tested instances, and, in average, we are ten times faster than alternative approaches. As we use a high level implementation language (AMPL) we should get further time improvements if lower level implementations are used (C, C++). Reproducibility of our results can be tested using our models and data available on-line at BPLIB.(1) (C) 2015 Elsevier Ltd. All rights reserved.