The lot-sizing and production scheduling problem in a real-life multi-product yoghurt production line is addressed. A new discrete/continuous time representation mixedinteger linear programming model, based on the definition of families of products, is presented. It is mainly optimized the packaging stage while timing and capacity constraints are imposed with respect to the pasteurization/homogenization and fermentation stage. Packaging units operate in parallel and may share common resources. Sequence-dependent times and costs are also explicitly taken into account. An industrial case study is presented wherein production bottlenecks are revealed and several retrofit design options are proposed to enhance the production capacity and flexibility of the plant.