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Unbalanced Assignment Problem Using Hungarian Method Lecture 03
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http://youtube.com/watch?v=49R8QHUFSAg
In this video you will learn about how to solve unbalanced Assignment problem using Hungarian method in Operation research. • After watching full video you will learn about • 1. How to solve assignment problem using Hungarian method? • 2. How to solve unbalanced assignment problem using Hungarian method? • _____________________________________________________________________________________ • SMALL CONTRIBUTION • SUBSCRIBE OUR CHANNEL AND SHARE OUR VIDEO WITH YOUR FRIENDS. • ______________________________________________________________________________________ • The assignment problems deal with the allocation problem in which the objective is to assign ‘n’ number of jobs to ‘n’ number of persons at a minimum cost or time. • Algorithm for Assignment Problem (Hungarian Method) • Step 1 • Prepare a Square Matrix:- If matrix is not square then make it square by adding dummy row or dummy column as required. • Step 2 • Reduce the matrix:- • 1.Row Reduction: Subtract smallest element of each row from all the elements of the respective row. • 2.Column Reduction: Subtract smallest element of each column from all the elements of the respective column. • In reduced matrix there should be one zero element in each row and each column. • Step 3 • Make an Assignment in the Reduced Matrix • 1. Row wise Assignment: Check all rows from top to bottom until a row with exactly one zero is found. Make an assignment to this single zero by making a square around it and cross all zeros in the corresponding column. • 2.Column wise Assignment: Check all columns from left to right until a column with exactly one zero is found. Make an assignment to this single zero by making a square around it and cross all zeros in the corresponding row. • Step 4 • Optimality Procedure • 1.If the number of Assignment = order of matrix then solution is optimal.( i.e. there is one assignment in each row and in each column) • 2.If the number of Assignment ≠ order of matrix then solution is not optimal. ( i.e. there is some row and column without assignment) • Step 5 • Revise New Cost Matrix: • Draw minimum number of horizontal and vertical lines necessary to cover all the zero in the reduced matrix by following steps: • 1.Mark (√) the rows in which there is no assignment. • 2.Check the marked row, if there is any zero elements occur in that row than mark the respective column. • 3.Check the marked column (√) if any assigned zero element occurs in those column than mark (√) the respective row. • 4.Draw straight line through all unmarked rows and marked columns. • Step 6 • Iterative towards the optimal solution: • 1.Examine the uncovered elements, select minimum uncovered elements. • 2.Subtract this minimum element from all the uncover elements. • 3.Add these minimum elements at the intersection of two straight lines. • 4.Leave the remaining elements as it is. • 5.By doing these we get new matrix for fresh assignment.(i.e. we get second basic feasible solution) • Step 7 • Repeat from step 3 to step 6 until number of Assignment = order of matrix. (i.e. there is one assignment in each row and in each column). • Useful for MBA, BBA, MCA, BE(Mechanical) students.. • Join this channel to get access to perks: • / @gouravmanjrekar • 👉 SUBSCRIBE : https://www.youtube.com/Gouravmanjrek... • 👆👆👆 • Join this channel to get access to perks: • / @gouravmanjrekar • 👉 SUBSCRIBE : https://www.youtube.com/Gouravmanjrek... • 👆👆👆
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