Minimal forecast horizons and a new planning procedure for the general dynamic lot sizing model: nervousness revisited

We show for the general dynamic lot sizing model how minimal forecast horizons may be detected by a slight adaptation of an earlier O(n log n) or O(n) forward solution method for the model. A detailed numerical study indicates that minimal forecast horizons tend to be small, that is, include a small number of orders. We describe a new planning approach to ensure stability of the lot sizing decisions over an initial interval of time or stability horizon in those (relatively rare) cases where no planning horizon is detected or where the stability horizon extends beyond the planning horizon. To this end, we develop a heuristic, but full horizon-based adaptation of the optimal lot sizing schedule, designed to minimize an upper bound for the worst-case optimality gap under the desired stability conditions. We also show how the basic horizon length n may be chosen to guarantee any prespecified positive optimality gap.