Analysis of a Forecasting-Production-Inventory System with Stationary Demand
研究一个按库存生产的单产品系统，需求平稳，利用预测更新信息改进生产决策，通过近似分析得到最优基库存水平的闭式表达式，揭示安全库存、随机需求、预测误差与产能限制之间的相互作用。
We consider a production stage that produces a single item in a make-to-stock manner. Demand for finished goods is stationary. In each time period, an updated vector of demand forecasts over the forecast horizon becomes available for use in production decisions. We model the sequence of forecast update vectors using the Martingale model of forecast evolution developed by Graves et al. (1986, 1998) and Heath and Jackson (1994). The production stage is modeled as a single-server, discrete-time, continuous-state queue. We focus on a modified base-stock policy incorporating forecast information and use an approximate analysis rooted in heavy traffic theory and random walk theory to obtain a closed-form expression for the (forecast-corrected) base-stock level that minimizes the expected steady-state inventory holding and backorder costs. This expression, which is shown to be accurate under certain conditions in a simulation study, sheds some light on the interrelationships among safety stock, stochastic correlated demand, inaccurate forecasts, and random and capacitated production in forecasting-production-inventory systems.