Mean flowtime and inventory in production systems:: A finite time analogue to Little's Law

Abstract

One of the most important results regarding flows in production systems is the well-known formula L=λ W , commonly referred to as “Little's Law”. Whereas the formula pertains to steady state averages, we show here that it has a finite analogue, i.e., there is another “law” for the case of a finite time interval. The analogue has practical economic value as it provides a precise reconciliation of average inventory and time-in-system over a finite time interval—sometimes more relevant than “steady state” averages. Examples of the usefulness of the law in practical managerial situations are provided. An additional result is to show how the analogue leads to a straightforward proof of Little's Law that requires minimal assumptions.