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:

88 | 93 | 60 |

22 | 14 | 62 |

27 | 26 | 79 |

**Subtract row minima**

We subtract the row minimum from each row:

28 | 33 | 0 | (-60) |

8 | 0 | 48 | (-14) |

1 | 0 | 53 | (-26) |

**Subtract column minima**

We subtract the column minimum from each column:

27 | 33 | 0 |

7 | 0 | 48 |

0 | 0 | 53 |

(-1) |

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

There are 3 lines required to cover all zeros:

27 | 33 | 0 | x |

7 | 0 | 48 | x |

0 | 0 | 53 | x |

**The optimal assignment**

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

27 | 33 | 0 |

7 | 0 | 48 |

0 | 0 | 53 |

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

88 | 93 | 60 |

22 | 14 | 62 |

27 | 26 | 79 |

The optimal value equals 101.

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