Mitigating Inventory Overstocking: Optimal Order-up-to Level to Achieve a Target Fill Rate over a Finite Horizon
Yinliang (Ricky) Tan, Anand A. Paul, Qi Deng, Lai Wei
Production and Operations Management · 2017 · Volume 26 · Issue 11
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 aninfiniteperformance review horizon. However, in practice, inventory managers are liable to maintain and report fill rates over afiniteperformance 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 aninfiniteperformance review horizon exceeds the expected fill rate assuming afiniteperformance 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.
Keywords
service level agreement, fill rate, positive lead time, base-stock policy, simulation-based optimization
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