Assigning resources to consumers according lists of preferences

Question

TLDR

I'm looking to assign resources from different categories to consumers, optimized according to some priorities linking consumers to resources.

Example

• The consumers are people, of which there are N_p.

• The resources are tickets (of which there are N_t in total) to different attractions (of which there are N_a), such as zoo, botanical gardens, museum, theatre, concert, etc.

• There is a limited number of tickets for any given attraction and these numbers may differ: say, 6 for the zoo, 20 for the gardens, 9 for the museum, etc.

  N_zoo + N_gardens + N_museum + N_theatre + ... = N_t

• Each person submits an ordered list of N_c < N_a choices of tickets they would like to receive.

• The total number of available tickets exceeds the number of people: N_t > N_p

• Each person must be assigned exactly one ticket.

• The aim is to maximize overall satisfaction in terms of people getting as close as possible to their preferred choices.

• Optional, second-order complications:

  • Couples, or even small groups of friends, might have to be assigned the same kind of ticket, either rigidly or by biasing the cost function.

  • Some people are premium members and some attractions are premium attractions: these premium members should get priority on the premium attractions, should they list them among their choices. Again, this might be done rigidly or by biasing the cost function.

The questions

• Is there a name for this sort of problem that would help me to look for relevant approaches in the literature?

• Can you suggest any algorithms particularly suited to this sort of problem?