To cope with the high labour costs of developed countries, and volatile market companies aim for flexible machines, that work in parallel in facilities that are dispersed geographically. This paper draws on an example from the food production industry, and investigates how production volumes should be allocated in a heterogeneous network of facilities with parallel machines. Apart from capacity costs, we entertain holding and backlog costs, which are significant due to the undesirability of storing perishable food products at the production facilities. Assuming that a weekly production schedule has been made for the network, we use an interior-point algorithm to optimize the production allocation. Our model takes into account three dimensions: the product, the facility, and the production line. For a network of three facilities, five production lines, and eight products, the optimisation procedure provides a cost reduction potential of 6.9% compared to the historical costs. Notably, the savings are realized by producing closer to the delivery date, as the inventory costs of fresh food products outweigh the savings of early production on more efficient equipment. Our contribution is threefold: First, the development of the optimisation procedure, second, the validation of the procedure against historical data, and third, evidence that fresh-food production should be responsive to demand and produce close to the delivery date, due to high inventory holding costs in comparison to the cost of capacity.