We consider an arbitrary supply chain structure under demand uncertainty. We look at a setting where the supply chain planning is executed periodically and where the demand of end items in subsequent periods is stochastic. In contrast to other linear programming-based approaches, we assume constant planned lead times. In this paper we discuss the timing of production during the planned lead times of items. If production starts immediately, the work-in-process inventory costs are higher, but producing later will result in higher safety stocks. We look at the influence of the demand variation, the planned lead time of the items, the utilization rate of resources, and the added value when merging items, on the inventory costs. The results indicate that, for higher utilization rates, producing early is more suitable.