Forecast horizons for a class of dynamic lot-size problems under discrete future demand

We present structural and computational investigations of a new class of weak forecast horizons – minimal forecast horizons under the assumption that future demands are integer multiples of a given positive real number – for a specific class of dynamic lot-size (DLS) problems. Apart from being appropriate in most practical instances, the discreteness assumption offers a significant reduction in the length of a minimal forecast horizon over the one using the classical notion of continuous future demands. We provide several conditions under which a discrete-demand forecast horizon is also a continuous-demand forecast horizon. We also show that the increase in the cost resulting from using a discrete minimal forecast horizon instead of the classical minimal forecast horizon is modest. The discreteness assumption allows us to characterize forecast horizons as feasibility/optimality questions in 0–1 mixed-integer programs. On an extensive test bed, we demonstrate the computational tractability of the integer programming approach. Owing to its prevalence in practice, our computational experiments emphasize the special case of integer future demands.