Inventory Service-Levels In The Customer Supply Chain

TLDR: 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.

Abstract: 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. Key words: Inventory management - Service levels - Customer order waiting time - Supply chain optimization