Concept explainers
Explanation of Solution
Given:
Five employees are available for performing four jobs. The time taken to perform each job by each of the person is given in the following table:
Time | (hours) | |||
Person | Job 1 | Job 2 | Job 3 | Job 4 |
1 | 22 | 18 | 30 | 18 |
2 | 18 | M | 27 | 22 |
3 | 26 | 20 | 28 | 28 |
4 | 16 | 22 | M | 14 |
5 | 21 | M | 25 | 28 |
To Determine:
Find an optimal assignment order of jobs to minimize the total time required for performing four jobs using Hungarian method.
Assignment of employees to jobs:
Step 1:
Add another column for Job 5 with zero costs, since the table is not balanced.
Time | (hours) | ||||
Person | Job 1 | Job 2 | Job 3 | Job 4 | Job 5 |
1 | 22 | 18 | 30 | 18 | 0 |
2 | 18 | M | 27 | 22 | 0 |
3 | 26 | 20 | 28 | 28 | 0 |
4 | 16 | 22 | M | 14 | 0 |
5 | 21 | M | 25 | 28 | 0 |
Step 2:
Take minimum from each row and subtract from the corresponding row. The new resultant table will be as follows:
Time | (hours) | ||||
Person | Job 1 | Job 2 | Job 3 | Job 4 | Job 5 |
1 | 22 | 18 | 30 | 18 | 0 |
2 | 18 | M | 27 | 22 | 0 |
3 | 26 | 20 | 28 | 28 | 0 |
4 | 16 | 22 | M | 14 | 0 |
5 | 21 | M | 25 | 28 | 0 |
Minimum | 16 | 18 | 25 | 14 | 0 |
Step 3:
Take minimum from each column and subtract from the corresponding column. The new resultant table will be as follows:
Time | (hours) | ||||
Person | Job 1 | Job 2 | Job 3 | Job 4 | Job 5 |
1 | 6 | 0 | 5 | 4 | 0 |
2 | 2 | M | 2 | 8 | 0 |
3 | 10 | 2 | 3 | 14 | 0 |
4 | 0 | 4 | M | 0 | 0 |
5 | 5 | M | 0 | 14 | 0 |
Step 4:
Draw minimum number of lines for covering all zeros in the resultant table...
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Chapter 7 Solutions
Operations Research : Applications and Algorithms
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