Analysis of a forecasting-production-inventory system with stationary demand

We consider a production stage that produces a single item in a make-to-sto ck manner. Demand for finished goods is stationary. In each time period, an updated vector of demand forecasts over the forecast horizon becomes avail able for use in production decisions. We model the sequence of forecast upd ate vectors using the Martingale model of forecast evolution developed by G raves et al. (1986, 1998) and Heath and Jackson (1994). The production stag e is modeled as a single-server, discrete-time, continuous-state queue. We focus on a modified base-stock policy incorporating forecast information an d use an approximate analysis rooted in heavy traffic theory and random wal k theory to obtain a closed-form expression for the (forecast-corrected) ba se-stock level that minimizes the expected steady-state inventory holding a nd backorder costs. This expression, which is shown to be accurate under ce rtain conditions in a simulation study, sheds some light on the interrelati onships among safety stock, stochastic correlated demand, inaccurate foreca sts, and random and capacitated production in forecasting-production-invent ory systems.