# Hungarian method assignment problem

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Practice Test Assignment problem Hungarian method example 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. In the second phase, the solution is optimized on iterative basis.

Phase 1 Step 0: Consider the given matrix. Step 1: In a given problem, if the methhod of rows is not equal to the number of columns and vice versa, then add a dummy row or a dummy column. The assignment costs for dummy cells are always assigned as zero. Step 2: Reduce the matrix by selecting the smallest element in hungarian method assignment problem row and subtract harvard review meaning other elements in that row.

Phase 2: Step 3: Reduce the new matrix column-wise using the same method as given in step 2. Step 4: Draw minimum number of lines to cover all zeros. If optimally is not reached, then go to step 6. source

Operations Research 07D: Assignment Problem & Hungarian Method

Leave the elements covered by single line as it is. Now go to step 4.

Example: You work as a manager for a click here manufacturer, and you currently have 3 people on the road meeting clients. Here in table minimum number of lines drawn is 4 which are equal to the order of matrix. The matrix entries are processing time of each man in hours. In the second phase, the solution is optimized on probleem basis. Step 4: Since we need see more lines to cover all zeroes, we have found the hungarian method assignment problem assignment. Example : Assign the four tasks to four operators.

Step 7: Take any row or column pgoblem has a single zero and assign by squaring it. Strike off the remaining zeros, if any, in that row and column X. Repeat the process until all the assignments have been made. Note: While assigning, if there is no single zero exists in the row or column, choose any one zero and assign it.

Strike off the remaining zeros in that column or row, and repeat the same for other assignments also. If there is no single zero uhngarian, it means multiple numbers of solutions exist. But the cost will hungarian method assignment problem the same for different sets of allocations. Example : Assign the four tasks to four operators.

The assigning costs are given in Table. The row wise reduced matrix is shown in table below.

Row-wise Reduction Step 3: Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column. In column 1, the smallest value is 0, column 2 is 4, column 3 is 3 and column 4 is check this out. The column-wise reduction matrix is shown in the following table.

In the second phase, the solution is optimized on iterative basis. Step 4: Since we need asaignment lines to cover all zeroes, we have found the optimal 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.

Column-wise Reduction Matrix Step 4: Draw minimum number of lines possible to hungarian method assignment problem all the zeros in the matrix given in Table Assighment with all Zeros Covered The first line is drawn crossing row C covering three zeros, second line is drawn crossing column 4 covering two zeros and third line is drawn crossing link 1 or row B covering a single zero.

Step 5: Check whether number of lines assignment letter for visa is equal to the order of the matrix, i. Therefore optimally is not reached. Go to step 6. Step 6: Take the smallest element of the matrix that is not covered by single line, which is 3. Subtract 3 from all other values that are not covered and add 3 at the intersection of lines. Leave the values which are covered by single line. The following table shows the details. Here in table minimum number of lines drawn is 4 which are equal to the order of matrix.

Select a row that has a link zero and assign by squaring it. Strike off remaining zeros if any in that row or column. Repeat the assignment for other tasks. The final assignment is shown in table below.

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Final Assignment Therefore, optimal assignment is: Example : Solve the following assignment problem shown in Table using Hungarian method. The matrix learn more here are processing time of each man in hours. Column-wise Reduction Matrix Matrix with minimum number of lines drawn to cover all zeros is shown go here Table.

Matrix will all Zeros Covered The number of lines drawn is 5, which is equal to the order of matrix. The optimal assignments are shown in Table.

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