# Answer to Question #31008 in Other Math for Sujata Roy

Question #31008

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)

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)

Expert's answer

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

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

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