Answer to Question #31008 in Math for Sujata Roy

Question

The optimal solution of the following
assignment problem using Hungarian
method is
I II III IV
A 8 26 17 11
B 13 28 4 26
C 38 19 18 15
D 19 26 24 10
(A) (B) (C) (D)
(A) (I) (II) (III) (IV)
(B) (I) (III) (II) (IV)
(C) (I) (III) (IV) (II)
(D) (I) (IV) (II) (III)

Answer 1

1) Rowand column Minimization
I II III IV
A 0 14 9 3
B 9 20 0 22
C 23 0 3 0
D 9 12 14 0
The optimal assignment is A→ I, B→ III, C→ II, D→ IV which is not cyclic

2)Row and column Minimization
(A) (B) (C) (D)
(A) (0) (0) (I) (II)
(B) (0) (I) (0) (II)
(C) (0) (I) (II) (0)
(D) (0) (II) (0) (I)
The optimal assignment is A→ B, B→ A, C→D, D→ C which is not cyclic