The Hungarian Method For The Assignment Problem

The Hungarian Method For The Assignment Problem-26
In row A, the smallest value is 13, row B is 15, row C is 17 and row D is 12.The row wise reduced matrix is shown in table below.

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You want to assign the employees to jobs in such a way that the overall cost is minimized.

This is an example of an assignment problem that we can use the Hungarian Algorithm to solve.

Write down the assignment results and find the minimum cost/time.

Note: While assigning, if there is no single zero exists in the row or column, choose any one zero and assign it.

An assignment problem can be easily solved by applying Hungarian method which consists of two phases.

In the first phase, row reductions and column reductions are carried out.The assignment costs for dummy cells are always assigned as zero.Select the smallest element of the whole matrix, which is NOT COVERED by lines.Now take out any dummy rows or columns that you added.The zeros in the final matrix correspond to the ideal assignment in the original matrix.Once we've done this, we make sure the number of rows equals the number of columns by adding dummy columns or rows with entries equal to the largest cost in the entire matrix.After we've got our square matrix, the steps of the algorithm are as follows: Once you can stop the algorithm, choose a set of zeros such that each row and column only has one zero selected.But the cost will remain the same for different sets of allocations.Reduce the matrix by selecting the smallest value in each row and subtracting from other values in that corresponding row.Subtract 3 from all other values that are not covered and add 3 at the intersection of lines. Here in table minimum number of lines drawn is 4 which are equal to the order of matrix. Strike off remaining zeros if any in that row or column. As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.

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