On order smoothing interpolating the order-up-to and constant order policies

We investigate order smoothing by interpolating two well-known inventory replenishment policies: the order-up-to policy and the constant order policy, as a means to improve supply chain performance. Order smoothing mitigates the bullwhip effect, reducing the risk of order fluctuations and inventory fluctuations for upstream supply chain echelons. Based on a two-echelon supply chain model, we explore the conditions under which order smoothing becomes desirable compared to situations without order smoothing, focusing on customer demand characteristics and smoothing strength. Our analysis examines both sinusoidal and stochastic responses to provide two distinct yet interrelated perspectives: amplitude in the frequency domain and the time domain. We highlight the significant impact of auto-correlated demand processes, which are prevalent in practice and relevant literature, on the economic benefits of order smoothing. Furthermore, we demonstrate that our proposed policy is an extension of the well-studied proportional order-up-to policy and can outperform it in certain scenarios.