This work considers the production scheduling of a real-life, consumer goods industry. The production facility consists of multiple continuous stages, and the packing stage constitutes the main production bottleneck. An immediate precedence and a unit-specific general precedence-based mixed integer linear programming (MILP) model are used to model the continuous packing stage. Constraints related to the operation of the previous production stages, in addition to maintenance restrictions, are also taken into account to avoid infeasible schedules. Two MILP-based decomposition strategies are proposed as the solution for realistic problem instances in acceptable computational times imposed by the plant. Scheduling solutions have been validated by the industry and directly compared with the schedules derived by the operators using simulation tools. Significant changeover time reductions are achieved, leading to improvements in the overall plant productivity. The proposed solution strategies could provide the basis for the development of a tool that will allow decision-makers to take quick and near-optimal scheduling decisions.