Measuring Item Fill-Rate Performance in a Finite Horizon

The standard treatment of fill rate relies on stationary and serially independent demand over an infinite horizon. Even if demand is stationary, managers are held accountable for performance over a finite horizon. In a finite horizon, the fill rate is a random variable. Studying the distribution is relevant because a vendor may be subject to financial penalty if she fails to achieve her target fill rate over a specified finite period. It is known that for a zero lead time, base-stock model, the expected value of a finite-horizon fill rate exceeds the long-run fill rate. In this paper, I investigate the behavior of the distribution of the finite-horizon fill rate when a stationary base-stock policy is used to control inventory. For a vendor facing a finite-horizon, fill-rate-level contract and using a stationary stocking policy, I examine how the the length of the review horizon (i.e., monthly or quarterly), the demand distribution, and the cost of failing to meet the target affect the stocking decision.