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:

76 | 87 | 13 | 30 |

66 | 48 | 16 | 42 |

43 | 8 | 1 | 37 |

85 | 33 | 49 | 64 |

**Subtract row minima**

We subtract the row minimum from each row:

63 | 74 | 0 | 17 | (-13) |

50 | 32 | 0 | 26 | (-16) |

42 | 7 | 0 | 36 | (-1) |

52 | 0 | 16 | 31 | (-33) |

**Subtract column minima**

We subtract the column minimum from each column:

21 | 74 | 0 | 0 |

8 | 32 | 0 | 9 |

0 | 7 | 0 | 19 |

10 | 0 | 16 | 14 |

(-42) | (-17) |

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

There are 4 lines required to cover all zeros:

21 | 74 | 0 | 0 | x |

8 | 32 | 0 | 9 | x |

0 | 7 | 0 | 19 | x |

10 | 0 | 16 | 14 | x |

**The optimal assignment**

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

21 | 74 | 0 | 0 |

8 | 32 | 0 | 9 |

0 | 7 | 0 | 19 |

10 | 0 | 16 | 14 |

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

76 | 87 | 13 | 30 |

66 | 48 | 16 | 42 |

43 | 8 | 1 | 37 |

85 | 33 | 49 | 64 |

The optimal value equals 122.

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