BalanceCast using SAT

[davidlang42]

1. Need to thoroughly test existing BalanceCast method:

• it may be okay in most instances or it may be rubbish
• investigate if theres any value to improving it with or without SAT

2. If re-writing BalanceCast to use SAT:

• BalanceCast probably needs its own engine type
• Will likely need a number of implementations (similar to SAT based selection engines)
• Should keep existing BalanceCast method as a heuristic-style option (in case SAT is too slow, or does weird things in some cases)

3. Basic method using SAT:

• only needs to calculate one cast group/cast at a time
• each applicant needs 1 var per role (R roles)
• within each non-multi section (or item), only 1 of an applicants vars can be true (or 0)
• for any roles which an applicant is NOT eligible or available for, assign var to false
• for any roles in adjacent items within non-consecutive item sections, each applicant can only have 1 var true (or 0)
• also needs something to ensure the correct number of people are picked for each role

4. Then to keep the talent even between roles....

• probably a branch and bound to minimise something like the difference in average suitability between role
• this is the hard bit, which probably varies between implementations