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:

3 | 74 | 60 |

3 | 55 | 64 |

85 | 96 | 1 |

**Subtract row minima**

We subtract the row minimum from each row:

0 | 71 | 57 | (-3) |

0 | 52 | 61 | (-3) |

84 | 95 | 0 | (-1) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 19 | 57 |

0 | 0 | 61 |

84 | 43 | 0 |

(-52) |

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

There are 3 lines required to cover all zeros:

0 | 19 | 57 | x |

0 | 0 | 61 | x |

84 | 43 | 0 | x |

**The optimal assignment**

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

0 | 19 | 57 |

0 | 0 | 61 |

84 | 43 | 0 |

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

3 | 74 | 60 |

3 | 55 | 64 |

85 | 96 | 1 |

The optimal value equals 59.

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