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 appr oach to ensure stability of the lot sizing decisions over an initial i nterval of time or stability horizon in those (relatively rare) cases where no planning horizon is detected or where the stability horizon e xtends beyond the planning horizon. To this end, we develop a heuristi c, but full horizon-based adaptation of the optimal lot sizing schedul e, designed to minimize an upper bound for the worst-case optimally ga p under the desired stability conditions. We also show how the basic h orizon length n may be chosen to guarantee any prespecified positive o ptimality gap.