This work addresses production and distribution planning for a real-world dairy supply chain. The planning model accounts for the production and distribution of Cheese, Yogurt, Powdered Milk and UHT milk products across a two-echelon Supply Chain. This task is undermined by the inherent variability of raw materials and finished products demand. The integrated production and distribution planning methodology introduced is based on a two-stage stochastic mixed integer linear programming formulation. In real-world settings the number of scenarios grows substantially; thus, a scenario reduction strategy based on clustering techniques is given. A decomposition and solving strategy is also introduced and applied to a real-world case study. This study showed that the value of the stochastic solution might rise to 21.1% above the deterministic solution. This indicates the importance of considering uncertainty for dairy production and distribution. Besides, different-size instances are tested to study the scalability of the solution approach.