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:

56 | 25 | 80 |

34 | 78 | 76 |

47 | 64 | 42 |

**Subtract row minima**

We subtract the row minimum from each row:

31 | 0 | 55 | (-25) |

0 | 44 | 42 | (-34) |

5 | 22 | 0 | (-42) |

**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:

31 | 0 | 55 | x |

0 | 44 | 42 | x |

5 | 22 | 0 | x |

**The optimal assignment**

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

31 | 0 | 55 |

0 | 44 | 42 |

5 | 22 | 0 |

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

56 | 25 | 80 |

34 | 78 | 76 |

47 | 64 | 42 |

The optimal value equals 101.

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