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:

17 | 1 | 10 | 64 |

56 | 71 | 81 | 4 |

36 | 34 | 2 | 61 |

82 | 10 | 90 | 13 |

**Subtract row minima**

We subtract the row minimum from each row:

16 | 0 | 9 | 63 | (-1) |

52 | 67 | 77 | 0 | (-4) |

34 | 32 | 0 | 59 | (-2) |

72 | 0 | 80 | 3 | (-10) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 0 | 9 | 63 |

36 | 67 | 77 | 0 |

18 | 32 | 0 | 59 |

56 | 0 | 80 | 3 |

(-16) |

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

There are 4 lines required to cover all zeros:

0 | 0 | 9 | 63 | x |

36 | 67 | 77 | 0 | x |

18 | 32 | 0 | 59 | x |

56 | 0 | 80 | 3 | x |

**The optimal assignment**

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

0 | 0 | 9 | 63 |

36 | 67 | 77 | 0 |

18 | 32 | 0 | 59 |

56 | 0 | 80 | 3 |

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

17 | 1 | 10 | 64 |

56 | 71 | 81 | 4 |

36 | 34 | 2 | 61 |

82 | 10 | 90 | 13 |

The optimal value equals 33.

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