In a supply chain network, satisfying the demand at the shop level while having a smooth production at the manufacturer (or plant) level are usually conflicting objectives. For instance, the production variations will be high if the shops can order exactly what they need and when they need it. On the other hand, producing the same amount each day prevents to adapt to the variations of the demand and may generate shortages or excess inventory. This study, performed in collaboration with a major fast-moving consumer goods company, proposes a lexicographic model for managing the supply chain in an integrated manner. Seven objective functions are considered to represent the goals of various stakeholders along the supply chain (from the shop to the plant) and different priority levels. A matheuristic combining both local-search procedures and exact methods is designed for scheduling the production orders and the shipments along the supply chain to optimize the overall cost structure. The proposed neighborhood structures employed in the local-search heuristics are able to perform dedicated modifications with respect to a single objective function (e.g., shortage, production variability, inventory level) and a single solution characteristic (e.g., production, shipment) without degrading the value of higher-level objectives. As computation time is limited, a time management approach for this method is proposed. Experiments are performed on 120 instances generated with the company to capture the real situations it faces. Using a rolling-window simulation with forecasted demands, we show that our method clearly outperforms a commercial solver and several common policies used in practice. The benefit of the proposed approach is highlighted both in terms of runtime and solution quality.