Existence of Forecast Horizons in Undiscounted Discrete-Time Lot Size Models

We are concerned with a discrete-time undiscounted dynamic lot size model in which demand and cost parameters are constant for an initial few periods. As our main result, we obtain an upper bound on the number of these periods which guarantees the optimality of the Economic Order Quantity (EOQ) as the size of the production lot to be produced in the first period. The upper bound is given and the optimality holds for every problem with an horizon not less than the upper bound and for the infinite horizon problem. The data beyond the upper bound are allowed to be specified arbitrarily. In the context of forecast horizon theory, we obtain conditions for a finite forecast horizon to exist in the undiscounted dynamic lot size model. Furthermore, existence results for forecast horizons in an undiscounted optimization problem are obtained for the first time in this paper.