An Assignment Optimization Task is a Transportation Task requires finding a maximum weight graph matching in a weighted bipartite graph.

## References

### 2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Assignment_problem Retrieved:2014-8-22.
• The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph.

In its most general form, the problem is as follows:

:There are 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 all tasks by assigning exactly one agent to each task and exactly one task to each agent in such a way that the total cost of the assignment is minimized.

If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called the linear assignment problem. Commonly, when speaking of the assignment problem without any additional qualification, then the linear assignment problem is meant.

Clean bathroom Sweep floors Wash windows
Jim \$3 \$3 \$3
Steve \$3 \$2 \$3
Alan \$3 \$3 \$2
• Then the Hungarian method, when applied to the above table would give us the minimum cost it can be done with: Jim cleans the bathroom, Steve sweeps the floors, and Alan washes the windows.