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:

57 | 72 | 55 | 80 |

41 | 26 | 6 | 25 |

23 | 31 | 30 | 73 |

35 | 48 | 53 | 96 |

**Subtract row minima**

We subtract the row minimum from each row:

2 | 17 | 0 | 25 | (-55) |

35 | 20 | 0 | 19 | (-6) |

0 | 8 | 7 | 50 | (-23) |

0 | 13 | 18 | 61 | (-35) |

**Subtract column minima**

We subtract the column minimum from each column:

2 | 9 | 0 | 6 |

35 | 12 | 0 | 0 |

0 | 0 | 7 | 31 |

0 | 5 | 18 | 42 |

(-8) | (-19) |

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

There are 4 lines required to cover all zeros:

2 | 9 | 0 | 6 | x |

35 | 12 | 0 | 0 | x |

0 | 0 | 7 | 31 | x |

0 | 5 | 18 | 42 | x |

**The optimal assignment**

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

2 | 9 | 0 | 6 |

35 | 12 | 0 | 0 |

0 | 0 | 7 | 31 |

0 | 5 | 18 | 42 |

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

57 | 72 | 55 | 80 |

41 | 26 | 6 | 25 |

23 | 31 | 30 | 73 |

35 | 48 | 53 | 96 |

The optimal value equals 146.

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