Example: Fighter Aircraft Problem – Linear
Assignment Method
From the original decision matrix
Fighter Aircraft Problem we can obtain attributewise preferences:
Rank 
f_{1} 
f_{2} 
f_{3} 
f_{4} 
f_{5} 
f_{6} 
weights 
0.2 
0.1 
0.1 
0.1 
0.2 
0.3 
1^{st} 
A2 
A2 
A3 
A3 
A3 
A1 
2^{nd} 
A4 
A3 
A1 A4 
A5 
A1 A4 
A3 
3^{rd} 
A1 
A4 

A1 

A2 A4 
4^{th} 
A3 
A1 
A2 
A2 
A2 

Three criteria f_{3},f_{5},
and f_{6} have tied attributewise rankings. These can be equalised:
Rank 
f_{31}f_{32} 
f_{51}f_{52} 
f_{61}f_{62} 
1^{st} 
A3 A3 
A3 A3 
A1 A1 
2^{nd} 
A1 A4 
A1 A4 
A3 A3 
3^{rd} 
A4 A1 
A4 A1 
A2 A4 
4^{th} 
A2 A2 
A2 A2 
A4 A2 
Each of these rankings gets half of
weight of the tied ranking and the matrix _{} is:

1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
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: (A_{3},A_{4},A_{1},A_{2}).