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:

23 | 24 | 96 | 5 |

98 | 23 | 39 | 9 |

93 | 61 | 14 | 37 |

93 | 7 | 85 | 78 |

**Subtract row minima**

We subtract the row minimum from each row:

18 | 19 | 91 | 0 | (-5) |

89 | 14 | 30 | 0 | (-9) |

79 | 47 | 0 | 23 | (-14) |

86 | 0 | 78 | 71 | (-7) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 19 | 91 | 0 |

71 | 14 | 30 | 0 |

61 | 47 | 0 | 23 |

68 | 0 | 78 | 71 |

(-18) |

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

There are 4 lines required to cover all zeros:

0 | 19 | 91 | 0 | x |

71 | 14 | 30 | 0 | x |

61 | 47 | 0 | 23 | x |

68 | 0 | 78 | 71 | x |

**The optimal assignment**

Because there are 4 lines required, the zeros cover an optimal assignment:

0 | 19 | 91 | 0 |

71 | 14 | 30 | 0 |

61 | 47 | 0 | 23 |

68 | 0 | 78 | 71 |

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

23 | 24 | 96 | 5 |

98 | 23 | 39 | 9 |

93 | 61 | 14 | 37 |

93 | 7 | 85 | 78 |

The optimal value equals 53.

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