Skip to content
Advertisements

QT/U4 Topic 6 Restriction in Assignment

It is sometimes possible that a particular person is incapable of doing certain work or a specific job cannot be performed on a particular machine. The solution of the assignment problem should take into account these restrictions so that the restricted (infeasible) assignment can be avoided. This can be achieved by assigning a very high cost (say ∞ or M)to the cells where assignments are prohibited, thereby restricting the entry of this pair of job-machine or resource-activity into the final solution.

Example : Five jobs are to be assigned to five men. The cost (in Rs.) of performing the jobs by each man is given in the matrix. The assignment has restrictions that Job 4 cannot be performed by Man 1 and Job 3 cannot be performed by Man 4 Find the optimal assignment of job and its cost involved.

Assignment Problem

topic 6.1.png

Solution: Assign large value to the restricted combinations or introduce ‘M’, see table.

Large Value Assignment to Restricted Combinations

topic 6.2.png

Reducing the matrix row-wise

topic 6.3.png

Reducing the matrix column-wise

topic 6.4.png

Draw minimum number of lines to cover all zeros, see Table.

All Zeros Covered

topic 6.5.png

Now, number of lines drawn = Order of matrix, hence optimality is reached. 
Allocating Jobs to Men.

Job Allocation to Men

topic 6.6.png

Assignment Schedule and Cost

topic 6.7.png

As per the restriction conditions given in the problem, Man 1 and Man 4 are not assigned to Job 4 and Job 3 respectively.

Advertisements
Advertisements
Advertisements

1 Comment »

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: