I've looked at Hungarian algorithm and Knapsack problems and neither quite hit the nail on the head. I've been trying to best rephrase my question while searching for answers and haven't got anywhere.
I have agents j and tasks i. Each agent can have between 1 and 4 task preferences (each with the cost 0-3), but must have only one task assigned by the end.
Each task also has a maximum number of agents that can be assigned to it (depending on the task).
Is there an algorithm out there that will minimise the overall cost, while maximising the amount of agents assigned to each task?
I hope that's clear, never really done this sort of thing before!