Optimizing Resident Schedules for Minimum Suffering

Consider the following problem:

A class of 6 ophthalmology residents need to work together to build their class' schedules for the upcoming year. Each resident's year is split into 6 periods called "rotations", where each rotation must be assigned to one of six sub-specialty positions (e.g. Retina, Cornea, Oculoplastics, etc.). The following constraints must be met:

• Each resident must complete each position exactly once at some point during the year
• No resident can be assigned to the same sub-specialty during the same rotation

Here's an example of a valid schedule grouping for this class of 6: