Note---Comments on the Optimality in "Optimal and System Myopic Policies for Multi-Echelon Production/Inventory Assembly Systems"

Schwarz and Schrage's model assumes that, for optimal policies in a multi-echelon production/inventory system, the lot size of a stage must not be larger than that of a predecessor stage, as lots move from the initial stage to the final stage. Examples in this Note illustrate that set-up costs and inventory holding costs may be such that optimal inventory policies exist when smaller lot sizes are produced intermittently at a stage, with an overlap, to feed the continuous production of a larger lot size at the next stage. Also, an example shows that, in contrast with another assumption in their model, optimality does not always require that the lot size at each stage be an integer multiple of the lot size at the successor stage.