Example:Fighter Aircraft Problem – Linear AssignmentMethod
From the original decision matrix Fighter Aircraft Problem we can obtain attributewise preferences:
Rank f1 f2 f3 f4 f5 f6
weights 0.2 0.1 0.1 0.1 0.2 0.3
1st A2 A2 A3 A3 A3 A1
2nd A4 A3 A1 A4 A5 A1 A4 A3
3rd A1 A4   A1   A2 A4
4th A3 A1 A2 A2 A2  

Three criteria f3,f5, and f6 have tied attributewise rankings. These can be equalised:
Rank f31f32 f51f52 f61f62
1st A3 A3 A3 A3 A1 A1
2nd A1 A4 A1 A4 A3 A3
3rd A4 A1  A4 A1 A2 A4
4th A2 A2  A2 A2 A4 A2

Each of these rankings gets half of weight of the tied ranking and the matrix is:
1st 2nd 3rd 4th
A1 0.3 0.15 0.45 0.1
A2 0.3 0 0.15 0.55
A3 0.4 0.4 0 0.2
A4 0 0.45 0.40 0.15

The LP formulation is:

The optimal solution is a permutation matrix P*:

The optimal order is than: (A3,A4,A1,A2).