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In this video you will learn about Assignment problem in Operation research multiple optimal solution by Hungarian method.
After watch full video you will learn about
1. How to solve assignment problem in operation research for multiple optimal solution by Hungarian method?
2. How to solve assignment problem when multiple optimal solution exist?
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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..

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Please watch: "UNBALANCED ASSIGNMENT PROBLEM IN OPERATION RESEARCH | USING HUNGARIAN METHOD | Lecture 03"
   • Unbalanced Assignment Problem | Using Hung...  
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