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Question
Solve the following minimal assignment problem :
| Machines | Jobs | ||
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
Solution
Given cost matrix is
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
Subtracting smallest element of each row from every element of that row.
| I | II | III | |
| M1 | 0 | 3 | 4 |
| M2 | 2 | 0 | 5 |
| M3 | 4 | 5 | 0 |
As each column contains a zero we do not subtract smallest element of a column from every element.
Hence allocation is as given below
Hence assignment is
M1 → I M2 → II M3 → III
Minimum total cost = 1 + 2 + 3
= 6 units.
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