Assignment Optimization Task
An Assignment Optimization is a Transportation Task requires finding a maximum weight graph matching in a weighted bipartite graph.
- See: Combinatorial Optimization, Matching (Graph Theory), Hungarian Algorithm, Minimum Cost Flow Problem, Linear Program, Simplex Algorithm, Quadratic Assignment Problem.
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.
- 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.
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Assignment_problem#Algorithms_and_generalizations Retrieved:2014-8-22.
- The Hungarian algorithm is one of many algorithms that have been devised that solve the linear assignment problem within time bounded by a polynomial expression of the number of agents.
The assignment problem is a special case of the transportation problem, which is a special case of the minimum cost flow problem, which in turn is a special case of a linear program. While it is possible to solve any of these problems using the simplex algorithm, each specialization has more efficient algorithms designed to take advantage of its special structure. If the cost function involves quadratic inequalities it is called the quadratic assignment problem.
- The Hungarian algorithm is one of many algorithms that have been devised that solve the linear assignment problem within time bounded by a polynomial expression of the number of agents.