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The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
Hungarian algorithm unbalanced assignment problem example: Image title: Worked example of minimising costs by assigning tasks to an unequal number of workers using the Hungarian method, by CMG Lee. Width: 100%: Height: 100%
This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem.
Harold William Kuhn (July 29, 1925 – July 2, 2014) was an American mathematician who studied game theory.He won the 1980 John von Neumann Theory Prize jointly with David Gale and Albert W. Tucker.
In the special case in which all the agents' budgets and all tasks' costs are equal to 1, this problem reduces to the assignment problem. When the costs and profits of all tasks do not vary between different agents, this problem reduces to the multiple knapsack problem. If there is a single agent, then, this problem reduces to the knapsack problem.
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