Hungarian Method For Assignment Problem

Hungarian Method For Assignment Problem-43
Algorithm : Step - 1 : Subtract the minimum element in each row from every entry in that row of a cost table.

Algorithm : Step - 1 : Subtract the minimum element in each row from every entry in that row of a cost table.

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Katta and Jay [7] presented the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. Mathematical Model Let be the cost of assigning the ith resource to the jth task.

Zhang and Bard [9] studied a multi-period assignment problem that arises as part of a weekly planning problem at mail processing and distribution centres. The Assignment Problem Suppose we have n resources to which we want to assign to n tasks on a one-to-one basis. We define the cost matrix to be the n × n matrix An assignment is a set of n entry positions in the cost matrix, no two of which lie in the same row or column.

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.

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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.

Now if there is a complete set of assignments with zero elements is possible than the resultant equivalent cost table is the optimal solution otherwise repeat this step( step 3).

The total cost of the optimal solution is the sum of amounts that have been subtracted from each row of the cost matrix.

Step 1: Subtract the smallest entry in each row from all the entries of its row. (2011) Adaptation and Fine-Tuning of the Weighted Sum Method on Personnel Assignment Problem with Hierarchical Ordering and Team Constraints.

Step 2: Subtract the smallest entry in each column from all the entries of its column. (2007) Workforce Optimization: Identification and Assignment of Professional Workers Using Constraint Programming. 26th International Symposium on Computer and Information Sciences, London, 26-28 September 2011, 571-576.

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