A prestressed precast beam is a type of beam that is stretched with traction elements. A common task in a factory of prestressed precast beams involves fulfilling, within a time horizon, the demand ordered by clients. A typical order includes beams of different lengths and types, with distinct beams potentially requiring different curing periods. We refer to the problem of planning such production as Heterogeneous Prestressed Precast Beams Multiperiod Production Planning (HPPBMPP). We formally define the HPPBMPP, argue its NP-hardness, and introduce four novel integer programming models for its solution and a size reduction heuristic (SRH). We propose six priority rules to produce feasible solutions. We perform computational tests on a set of synthetic instances that are based on data from a real-world scenario and discuss a case study. Our experiments suggest that the models can optimally solve small instances, while the SRH can produce high-quality solutions for most instances.