FFXIV static composition solver

We have a bunch of people and need to figure out what role they'll play in our static. How do we decide?

Role categorization

First, we define the roles as they are in FFXIV (not exhaustive):

{
  "ranged dps": ["BRD", "MCH", "DNC", "BLM", "RDM", "SMN"],
  "melee dps": ["DRG", "MNK", "SAM", "NIN", "RPR"],
  "tank": ["GNB", "PLD", "WAR", "DRK"],
  "barrier healer": ["SCH", "SGE"],
  "pure healer": ["WHM", "AST"],
  "mage": ["BLM", "RDM", "SMN"],
  "ranged physical": ["DNC", "BRD", "MCH"]
}

Desired composition

We also need to specify our desired composition as pairs of roles to how many slots of that role to fill:

{
  "ranged dps": 2,
  "melee dps": 2,
  "tank": 2,
  "barrier healer": 1,
  "pure healer": 1,
}

Player preferences

Each player lists the jobs they're willing and able to play, ranked in order of preference. This can be compiled into a preferences data structure like so:

{
  "Yorvo Hawke": ["DRG", "GNB"],
  "Squidgy Bunny": ["NIN", "SMN", "WHM", "PLD"],
  "Renfleur Orinoux": ["DRK", "SAM"],
  "Zelle Tamjin": ["PLD", "BLM"],
  "Era Dere": ["WHM", "DNC"],
  "Brando Id": ["SCH"],
  "Alleriana Valyrian": ["RDM", "BLM"],
  "Reye Fenris": ["BRD", "DRG"],
}

Desired output

Phase 1

To start, we're looking for any valid output that fills each desired role, e.g.

{
  "Yorvo Hawke": "DRG",
  "Squidgy Bunny": "NIN",
  "Renfleur Orinoux": "DRK",
  "Zelle Tamjin": "PLD",
  "Era Dere": "WHM",
  "Brando Id": "SCH",
  "Alleriana Valyrian": "RDM",
  "Reye Fenris": "BRD",
}

Phase 2

What determines the "best" fit? We can tune our algorithm to prioritize job assignments in different ways.

For example, is it better to have 7 people with their 1st choice and 1 person with their 8th choice, or 8 people with their 2nd choice? Let's iterate on the algorithm to see what we can come up with.