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Question
Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.
Service Time ( in hrs.)
| Counters | Salesmen | |||
| A | B | C | D | |
| W | 41 | 72 | 39 | 52 |
| X | 22 | 29 | 49 | 65 |
| Y | 27 | 39 | 60 | 51 |
| Z | 45 | 50 | 48 | 52 |
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Solution
This problem is already 4 x 4.
Select the smallest element in each row and subtract it from every element in each row :
Select the smallest element in each column of the above matrix and subtract it form every element in that column.
Draw the minimum lines covering all zeros.
Minimum lines covering all zeros is not equal to the order of the matrix.
Minimum uncovered value 2 is subtracted from uncovered values and added to values at intersection of the lines.
Draw minimum lines covering all the zeros.
Minimum lines covering all the zeros equal to the order of the matrix.
∴ Allocation of counters can be done.
The allocation of the counters to the salesmen is
W → C, X → B, Y → A, Z → D
The minimum time = 39 + 29 + 27 +52 = 147 Hrs.
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Step III: Draw the minimum number of lines to cover all zeros.
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C →IV D →`square`
Total minimum time = `square` hours.
