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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

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I II III IV
A 8 26 17 11
B 13 28 4 26
C 38 19 18 15
D 19 26 24 10

Step 1:Identity the minimum element in each row and subtract it from every element of that row

 I II III Iv A 0 18 9 3 B 9 24 0 22 C 23 4 3 0 D 9 16 14 0

Step 2:Identity the minimum element in each column and subtract it from every element of that column

 I II III Iv A 0 14 9 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0

Step 3:Cover all 0's with a minimum number of lines

 I II III Iv A 0 14 9 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0

Step 4: (Optimal Assignment) There are 4 lines required.The 0's covers an optimal assignment.

 I II III Iv A 0 14 9 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0

This corresponds to the following optimal assignment in original cost matrix

 I II III Iv A 8 26 17 11 B 13 28 4 26 C 38 19 18 15 D 39 26 24 10

The total cost of assignment=A(I) +B(III)+C(II)+D(Iv)=8+19+4+10=41

Hence,Option(B) A(I) B(III) C(II) D(Iv)is the correct choice here.

http://www.hungarianalgorithm.com/solve.php (Online Calculator)

by Boss (40.8k points)
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Hi Leen tell me seriously how much time did you take to solve it .....Great efforts
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Hello shekhar chauhan this topic was new for me. first i read about it from different-2 sources.After i solved it on white paper then i made this content.I took almost half an hour on it. i think that was too much

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this topic from which subject?

ANS IS B

by Boss (48.2k points)

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