Discussion of the standard processing time

The input-weighted average standard processing time for a multi-item machine is discussed in this paper. For practical purposes it is important to have a short average processing time. It is shown that the input-weighted average processing time does not depend on the scheduling, sequencing and lot-sizing; it is only influenced by the total input and by the individual standard processing times. Furthermore, the relationship between the individual standard processing time and the average standard processing time is investigated. It is proven that the input-weighted average standard processing time is a convex function of the standard processing time of one certain item. An interesting consequence of the convexity is the fact that a decrease of the standard processing time of an item with a standard processing time less than half of the input-weighted average standard processing time causes an increase of the input-weighted average processing time.