Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given.

Fill in the cost matrix (random cost matrix):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

This is the original cost matrix:

55 | 58 | 97 |

76 | 10 | 99 |

14 | 74 | 39 |

**Subtract row minima**

We subtract the row minimum from each row:

0 | 3 | 42 | (-55) |

66 | 0 | 89 | (-10) |

0 | 60 | 25 | (-14) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 3 | 17 |

66 | 0 | 64 |

0 | 60 | 0 |

(-25) |

**Cover all zeros with a minimum number of lines**

There are 3 lines required to cover all zeros:

0 | 3 | 17 | x |

66 | 0 | 64 | x |

0 | 60 | 0 | x |

**The optimal assignment**

Because there are 3 lines required, the zeros cover an optimal assignment:

0 | 3 | 17 |

66 | 0 | 64 |

0 | 60 | 0 |

This corresponds to the following optimal assignment in the original cost matrix:

55 | 58 | 97 |

76 | 10 | 99 |

14 | 74 | 39 |

The optimal value equals 104.

HungarianAlgorithm.com © 2013-2017