Pipkins' advanced schedule optimization is based on a Sum of Squares figure of merit analysis, not a simple "hours-net-to-zero." Competing algorithms that use the net-to-zero approach cannot distinguish between schedules that deliver good and bad service. Only Pipkins' algorithms can truly optimize. The Scheduler uses this algorithm to maximize the achievable quality of service. The algorithm takes the difference between required and provided staff for each schedule time step interval during the period to be scheduled, then squares and sums each figure to determine the sum of squared differences. The Scheduler works to minimize this figure for a time step, for the total day, and for the entire date range being scheduled. For example:

By adjusting start/stop times and lunch/break times, the scheduler lowers the SSQ until the schedule is optimized for each time step. This method of assessing a schedule's accuracy offers two advantages:

• Because the differences are squared before summed, staffing excesses and deficiencies do not cancel each other as they would if they were simply added.
  
  
• The relationship between staff numbers and quality of service is non-linear, and is best represented by the squaring function. For example, as 2 squared is 4, the Scheduler regards a staffing deficiency of 2 as being 4 times as bad as a deficiency of 1. This is a fair reflection of the expected reduction in service.