Utilizing Forecast Band Refinement for Capacitated Production Planning

Abstract
We present a model for forecast evolution that captures two notions related to forecasts: (1) forecasts are not exact; (2) forecasts over longer horizons are less certain than those over shorter horizons. We model the forecast of discrete demand as a band defined by the lower and upper bounds on demand, such that future forecasts lie within the current band. We develop a capacitated production planning model for a single product with terminal demand. We develop four heuristics for the problem and characterize their performance. In particular, two of the heuristics are optimal for the no holding-cost case. In our computational study, we analyze the performance of our heuristics and compare them to the optimal solution and to a simple heuristic that simulates common industrial practice using point forecasts. We find that two of our heuristics are very close to the optimal solution (less than 0.5% away from optimal on average under the conditions studied). Further, we consider forecast update patterns with primarily early, intermediate, and late information updates and provide insights on the effect of information update patterns on optimal costs.