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Unbalanced Assignments

The aspect of assignment problem has a huge role to play given its importance in the branch of operations research.  Hence, it can be seen that certain rules and regulations are to be followed while charting out the assignment problem. Once they are not in tune with each other, there are high chances that they do not yield the correct results. Hence, in case of any discrepancy, it has to be solved by framing a correct equation keeping in mind the details.

An unbalanced assignment is a situation where, this number of rows cannot be equated with the number of columns in case of an assignment matrix column. When this assignment cost matrix is not taken as a square matrix, and the number of sources does not match up to number of destinations, an unbalanced state comes to the fore. With an unbalanced assignment, a rectangular matrix is to be dealt with.

Since no solution can be obtained before getting equal amount on both the sides so dummy rows and columns are added. There is no extra associated cost with this addition, and the primary aim is to get a perfect defective function that matches up the solution.

Example: Let us take an example of a machinejob issue. If it is found that the number of machines is greater than the number of jobs that are given, then to equate the sides, a number of dummy jobs are created that can make both the sides equal and it is taken that no additional cost is associated.

This equation is extremely important for students to get a better idea of this problem. Here are some of the sums that students should solve to get a better idea.

 

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