  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 DGPs 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.
