On the time-window fulfillment rate in a single-item min-max inventory control system

This paper considers an inventory control system with a constraint on the service level. We focus on a popular service target in practice, the time-window ready rate, which is defined as the percentage of periods in which demands are completely fulfilled within a pre-specified time window. We explore the cost impact of different time-window ready rate settings by proposing evaluation and optimization methods for a single-location single-item min-max (or (s, S)) inventory system. New optimization procedures have been developed because the existing methods, which are based on a Lagrangian multiplier, cannot generally handle the current problem. More specifically, in some cases the time-window ready rate is a complicated function of the re-order point s, which renders existing algorithms inapplicable. Our algorithms are based on the monotone properties of cost and service constraint functions, which allow us to search the optimal policy efficiently within an identified region of policy-parameter values. Numerical experiments show the non-linear trade-off between cost and service, and indicate that extending or shrinking the time window can have a significant impact on the inventory cost. © 2005 "IIE".