Method and apparatus for reducing scheduling conflicts for a resource

A system, comprising:

• a resource for processing a workpiece;
• and
• at least one scheduling agent configured to provide a schedule of engagements for a resource, each engagement having a working window and an associated engagement density function, combine the engagement density functions of the scheduled engagements to generate a committed capacity function for the resource, identify a region of violation in the committed capacity function where the committed capacity of the resource exceeds a capacity threshold, determine an area of a region of overlap between the working window of a selected engagement and the region of violation, determine an area reduction amount for the selected engagement based on a portion of the area of the region of overlap less than the total area of the region of overlap, and change the working window of the selected engagement based on the area reduction amount.