Mitigating Inventory Overstocking: Optimal Order‐up‐to Level to Achieve a Target Fill Rate over a Finite Horizon

Abstract

Service level agreements (SLAs) are widely adopted performance‐based contracts in operations management practice, and fill rate is the most common performance metric among all the measurements in SLAs. Traditional procedures characterizing the order‐up‐to level satisfying a specified fill rate implicitly assume an infinite performance review horizon. However, in practice, inventory managers are liable to maintain and report fill rates over a finite performance review horizon. This horizon discrepancy leads to deviation between the target fill rate and actual achieved fill rate. In this study, we first examine the behavior of the fill rate distribution over a finite horizon with positive lead time. We analytically prove that the expected fill rate assuming an infinite performance review horizon exceeds the expected fill rate assuming a finite performance review horizon, implying that there exists some inventory “waste” (i.e., overstocking) when the traditional procedure is used. Based on this observation and the complexity of the problem, we propose a simulation‐based algorithm to reduce excess inventory while maintaining the contractual target fill rate. When the lead time is significant relative to the length of the contract horizon, we show that the improvement in the inventory system can be over 5%. Further, we extend our basic setting to incorporate the penalty for failing to meet a target, and show how one can solve large‐scale problems via stochastic approximation. The primary managerial implication of our study is that ignoring the performance review horizon in an SLA will cause overstocking, especially when the lead time is large.