Question
Solve the following minimal assignment problem and hence find the minimum value :
I | II | III | IV | |
A | 2 | 10 | 9 | 7 |
B | 13 | 2 | 12 | 2 |
C | 3 | 4 | 6 | 1 |
D | 4 | 15 | 4 | 9 |
Solution
I | II | III | IV | |
A | 2 | 10 | 9 | 7 |
B | 13 | 2 | 12 | 2 |
C | 3 | 4 | 6 | 1 |
D | 4 | 15 | 4 | 9 |
Subtracting minimum element from each row,
we have
I | II | III | IV | |
A | 0 | 8 | 7 | 5 |
B | 11 | 0 | 10 | 0 |
C | 2 | 3 | 5 | 0 |
D | 0 | 11 | 0 | 5 |
Subtracting minimum element from each
Column, we have
I | II | III | IV | |
A | 0 | 8 | 7 | 5 |
B | 11 | 0 | 10 | 0 |
C | 2 | 3 | 5 | 0 |
D | 0 | 11 | 0 | 5 |
Hence A → I, B → II, C → IV, D → III
Minimum value is 2 + 2 + 1 + 4 = 9
Is there an error in this question or solution?
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Solution Solve the Following Minimal Assignment Problem and Hence Find the Minimum Value : Concept: Assignment Problem.