On non-negative auto-correlated integer demand processes

Methods to generate realistic non-stationary demand scenarios are a key component for analyzing and optimizing decision policies in supply chains. Typical forecasting techniques recommended in standard inventory control textbooks consist of some form of simple exponential smoothing (SES) for both the estimates for the mean and standard deviation. We study demand generating processes (DGPs) that yield non-stationary demand scenarios, and that are consistent with SES, meaning that SES yields unbiased estimates when applied to the generated demand scenarios. As demand in typical practical settings is discrete and non-negative, we study consistent DGPs on the non-negative integers. We derive conditions under which the existence of such DGPs can be guaranteed, and propose a specific DGP that yields autocorrelated, discrete demands when these conditions are satisfied. Our subsequent simulation study gains further insights into the proposed DGP. It demonstrates that from a given initial forecast, our DGP yields a diverse set of demand scenarios with a wide range of properties. To show the applicability of the DGP, we apply it to generate demand in a standard inventory problem with full backlogging and a positive lead time. We find that appropriate dynamic base-stock levels can be obtained using a new and relatively simple algorithm, and we demonstrate that this algorithm outperforms relevant benchmarks.