Hungarian Algorithm Calculator

Hungarian algorithm is used for the optimal assignment of jobs to workers in one-to-one manner and to reduce the cost of the assignment. In this calculator, you can solve the work assignment problem with the hungarian algorithm.

Job / Work Assignment Problem Calculation

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Example:

Consider there are 3 jobs, should be assigned to 3 workers (one job to each). The cost of assigning the jobs are :

Jobs/Man J1 J2 J3
M1 52 19 20
M2 8 83 24
M3 42 35 89

Step 1 :

Subtract row minima,
Subtract the minimum value of the row from other values.

Jobs/Man J1 J2 J3 Row Minima
M1 33 0 1 -19
M2 0 75 16 -8
M3 7 0 54 -35

Step 2 :

Subtract column minima,
Subtract the minimum value of the column from other values.

Jobs/Man J1 J2 J3
M1 33 0 0
M2 0 75 15
M3 7 0 53
Col. Minima -1

Step 3 :

Cover all zeros with a minimum number of lines,


Jobs/Man J1 J2 J3
M1 33 0 0
M2 0 75 15
M3 7 0 53

Step 4 :

Choose zero's


Jobs/Man J1 J2 J3
M1 33 0 0
M2 0 75 15
M3 7 0 53

Step 5 :

Apply the selection to the original matrix, that will be the jobs assigned to them and adding cost of all assigned jobs will be the minimum cost.


Jobs/Man J1 J2 J3
M1 52 19 20
M2 8 83 24
M3 42 35 89

Job Assignment Problem with concept of Hungarian algorithm is made easier here.

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