Analysis of a Forecasting-Production-Inventory System with Stationary Demand

Abstract

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. (1986Graves et al. ( , 1998 and Heath and Jackson (1994). The production stage is modeled as a single-server discrete-time continuous-state queue. We focus on the stationary version of a class of policies that is shown to be optimal in the finite time horizon, deterministic-capacity case, 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.

Effective Heuristics for Capacitated Production Planning with Multiperiod Production and Demand with Forecast Band Refinement

“…Our insight is similar in spirit to the one presented by Toktay and Wein (2001), where they indicate that receiving information earlier is more valuable in highutilization scenarios, although the incremental value of this information decreases with capacity utilization under heavy-traffic approximations. Similarly, Karaesmen et al (2002a, b) show that for a capacitated production-inventory system where advance orders are known exactly within a fixed forecast window, advance order information beyond a certain leadtime has no incremental value.…”

“…Ozer (2001, 2003) study optimal replenishment policies for single and multiechelon uncapacitated inventory systems with advance demand information. Toktay and Wein (2001) consider an MMFE model and characterize effective policies under heavy-traffic assumptions for a capacitated single server. They investigate the quality of a dynamically evolving forecast, the impact of capacity utilization, and the impact of demand correlation.…”

To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating

“…Our paper most closely follows the Markovian forecast revision approach, as developed by [16] and later extended by [17] and [11]. The Markovian forecast revision approach has been commonly adopted in the operations literature, e.g., [6,7,12,22,31].…”

Inventory Management: Information, Coordination, and Rationality

“…A group of scholars have incorporated the dynamic nature of forecast revisions into inventory control problems. Papers in this group include those of Hausman (1969), Graves et al (1986), Heath and Jackson (1994), Güllü (1996) and Toktay and Wein (2001). All of these works show that incorporating demand updates to control problems reduces the cost of managing inventories by proposing control methods that are responsive to forecast information.…”