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Question
Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.
| Machine | ||||
| U | V | W | ||
| Jobs | A | 17 | 25 | 31 |
| B | 10 | 25 | 16 | |
| C | 12 | 14 | 11 | |
(cost is in ₹ per unit)
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Solution
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1: Select the smallest element in each row and subtract this from all the elements in its row.
| Machine | ||||
| Jobs | U | V | W | |
| A | 2 | 0 | 16 | |
| B | 0 | 15 | 6 | |
| C | 1 | 3 | 0 | |
Look for atleast one zero in each row and each column.
Here each and every row and columns having exactly one zero No need step 2 go to step 3.
Step 3:
| Machine | ||||
| Jobs | U | V | W | |
| A | 2 | 0 | 16 | |
| B | 0 | 15 | 6 | |
| C | 1 | 3 | 0 | |
Mark the zero by □ Mark other zeros in its column by X.
Since each row and each column contains exactly one assignment, all the three machine have been assigned a job.
| Job | Machine | Cost |
| A | V | 15 |
| B | U | 10 |
| C | W | 11 |
| Total Cost | 46 | |
The Optimal assignment (minimum) cost = 46
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