Production Planning
Displacement wastes nothing — the transitional mixture goes onto yarn that accepted either recipe. Only the clock decides.
— h
To bring the box inside tolerance without draining
Displacement is only available when both recipes are chemically compatible, and that is a formulation judgement rather than an arithmetic one — mixing incompatible binders can gel the box, which costs far more than the drain it was avoiding. A negative time saving simply means draining is quicker for this pair. The exponential also assumes the box is well stirred and the addition is fresh recipe at working concentration; boxes with poor circulation retain old size in corners and on immersed rollers. Whatever the sequence, the yarn made during the transition carries an intermediate size add-on and should be tracked, since weaving performance follows size pick-up closely.
Sizing Batch Washout & Size Box Changeover Optimizer — free, with the formula and a worked example, at Textile School.