Assignment problem

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The assignment problem is a fundamental combinatorial optimization problem.
In its most general form, the problem is as follows:

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.

It is required to perform as many tasks as possible by assigning at most one agent to
each task and at most one task to each agent,
in such a way that the total cost of the assignment is minimized.

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In applied mathematics, the maximum generalized assignment problem is a problem
in combinatorial optimization.
This problem is a generalization of the assignment problem in which
both tasks and agents have a size.

Moreover, the size of each task might vary from one agent to the other.

[kongp]

Appreciated in Carrier and Life of Mathematic Specialist .