update Mikhail Rudoy make me realize that I partially wrongly reduced the problem.I am interested in the following variation of the assignment problem:The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. Each task have a maximal capacity for the amount of agent that are assigned to. It is required to perform all tasks by assigning exactly k task to each agent in such a way that the total cost of the assignment is minimized and the tasks capacities are satified.Can it be reduced to the standard assignment problem or any other well known algorithm ?
one-to-k assignment problem with jobs capacities
reductions