Forecast Horizons in the Discounted Dynamic Lot Size Model

We derive a sharp upper bound on the minimal forecast horizon in the discounted dynamic lot size model with constant initial demand. This bound is given by m(m + 1), where m is the EOQ's worth, i.e., the number of periods for which the total demand equals Economic Order Quantity. Our results do not require the solution of the infinite horizon problem to be unique. Nor do they require the infinite horizon problem to be well defined. We also prove some sensitivity results with respect to the discount factor and the setup cost.