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:

73 | 7 | 43 | 93 |

7 | 7 | 57 | 40 |

37 | 50 | 27 | 67 |

50 | 9 | 77 | 28 |

**Subtract row minima**

We subtract the row minimum from each row:

66 | 0 | 36 | 86 | (-7) |

0 | 0 | 50 | 33 | (-7) |

10 | 23 | 0 | 40 | (-27) |

41 | 0 | 68 | 19 | (-9) |

**Subtract column minima**

We subtract the column minimum from each column:

66 | 0 | 36 | 67 |

0 | 0 | 50 | 14 |

10 | 23 | 0 | 21 |

41 | 0 | 68 | 0 |

(-19) |

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

There are 4 lines required to cover all zeros:

66 | 0 | 36 | 67 | x |

0 | 0 | 50 | 14 | x |

10 | 23 | 0 | 21 | x |

41 | 0 | 68 | 0 | x |

**The optimal assignment**

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

66 | 0 | 36 | 67 |

0 | 0 | 50 | 14 |

10 | 23 | 0 | 21 |

41 | 0 | 68 | 0 |

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

73 | 7 | 43 | 93 |

7 | 7 | 57 | 40 |

37 | 50 | 27 | 67 |

50 | 9 | 77 | 28 |

The optimal value equals 69.

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