Hungarian Method For Assignment Problem

Hungarian Method For Assignment Problem-6
Step - 3 : Draw a set of minimum number of lines through some of the rows and columns in such a way as to cover all the zeros.Subtract the minimum element from every element without a line through them and then add that minimum element that lies at the intersection of two lines.I solved it using the Hungarian method but for job A and D I had only one zero that too in the same column.

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The assignment problem can be written mathematically as: Minimize 2.3.

Hungarian Method The following algorithm applies the above theorem to a given n × n cost matrix to find an optimal assignment.

The assignment problem, also known as the maximum weighted bipartite matching problem, is a widely-studied problem applicable to many domains, specifically for maximization of output or minimization of cost.

It can be stated as follows: given a bipartite graph made up of two partitions V and U, and a set of weighted edges E between the two partitions, the problem requires the selection of a subset of the edges with a maximum sum of weights such that each node or is connected to at most one edge.

All the algorithms developed to find optimal solution of transportation problem are applicable to assignment problem.

However, due to its highly degeneracy nature, a specially designed algorithm widely known as Hungarian method proposed by Kuhn [1] is used for its solution.Suppose also that we know the cost of assigning a given resource to a given task. The sum of the n entries of an assignment is its cost.An assignment with the smallest possible cost is called an optimal assignment.Algorithm : Step - 1 : Subtract the minimum element in each row from every entry in that row of a cost table.Step - 2 : Subtract the minimum element in each column from every entry in that column of the resulting equivalent cost table. Content Header .feed_item_answer_user.js-wf-loaded . Assignment of jobs to workers, contract to contractors undergoing a bidding process, assigning nurses to duty post, or time tabling for teachers in school and many more have become a growing concern to both management and sector leaders alike.This step results in at least one zero in every row and column.If there is a complete set of assignments with zero elements is possible than the resultant equivalent cost table is the optimal solution otherwise go to next step.The problem may also be phrased as a minimization problem by considering, instead of edge weights, a set of non-negative edge costs, , where W is at least as large as the maximum of all the edge weights.It can also be stated as: how to determine the best possible assignment of workers to jobs, such that the total ratings are maximized [2] . Related Works Franses and Gerhard [3] studied an assignment problem particular to the personnel scheduling of organisations such as laboratories.


Comments Hungarian Method For Assignment Problem

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    This problem is Kuhn’s Hungarian method Kuh55. This method is of major theoretical interest and is still used widely. It maintains a price for each object and an incomplete assignment of persons and objects. At each iteration, the method chooses an unassigned person and computes a shortest augmenting path from this person to the set of unassigned objects, using reduced costs as arc.…

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    The assignment problem is a special case of the transportation problem, which in turn is a special case of the min-cost flow problem, so it can be solved using algorithms that solve the more general cases. Also, our problem is a special case of binary integer linear programming problem which is NP-hard. But, due to the specifics of the problem, there are more efficient algorithms to solve it.…

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