Summary: In this paper we consider an inventory location that serves downstream nodes (e.g. production processes, regional warehouses or customers) in a supply chain. It is pointed out, that the overall optimization of logistical processes should be based on the order delivery time as a critical unifying dimension. It is shown that the standard \(\alpha\)-, \(\beta\)- and \(\gamma\)-service-levels used in inventory theory, when considered from the point of view of a downstream node in the supply chain, provide only limited information about the delay the orders observe. A procedure for the determination of the probability distribution of the order waiting time in a discrete time periodic \((r,S)\)-inventory system is developed. Implications for the optimization of sub-processes in the supply chain are discussed.