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 | 80 | 24 | 68 |

45 | 87 | 47 | 59 |

29 | 33 | 38 | 65 |

15 | 16 | 66 | 3 |

**Subtract row minima**

We subtract the row minimum from each row:

0 | 57 | 1 | 45 | (-23) |

0 | 42 | 2 | 14 | (-45) |

0 | 4 | 9 | 36 | (-29) |

12 | 13 | 63 | 0 | (-3) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 53 | 0 | 45 |

0 | 38 | 1 | 14 |

0 | 0 | 8 | 36 |

12 | 9 | 62 | 0 |

(-4) | (-1) |

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

There are 4 lines required to cover all zeros:

0 | 53 | 0 | 45 | x |

0 | 38 | 1 | 14 | x |

0 | 0 | 8 | 36 | x |

12 | 9 | 62 | 0 | x |

**The optimal assignment**

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

0 | 53 | 0 | 45 |

0 | 38 | 1 | 14 |

0 | 0 | 8 | 36 |

12 | 9 | 62 | 0 |

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

23 | 80 | 24 | 68 |

45 | 87 | 47 | 59 |

29 | 33 | 38 | 65 |

15 | 16 | 66 | 3 |

The optimal value equals 105.

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