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:

8 | 38 | 2 |

20 | 14 | 73 |

1 | 94 | 64 |

**Subtract row minima**

We subtract the row minimum from each row:

6 | 36 | 0 | (-2) |

6 | 0 | 59 | (-14) |

0 | 93 | 63 | (-1) |

**Subtract column minima**

Because each column contains a zero, subtracting column minima has no effect.

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

There are 3 lines required to cover all zeros:

6 | 36 | 0 | x |

6 | 0 | 59 | x |

0 | 93 | 63 | x |

**The optimal assignment**

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

6 | 36 | 0 |

6 | 0 | 59 |

0 | 93 | 63 |

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

8 | 38 | 2 |

20 | 14 | 73 |

1 | 94 | 64 |

The optimal value equals 17.

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