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:

46 | 60 | 77 | 2 |

18 | 74 | 61 | 35 |

41 | 92 | 24 | 2 |

74 | 93 | 72 | 44 |

**Subtract row minima**

We subtract the row minimum from each row:

44 | 58 | 75 | 0 | (-2) |

0 | 56 | 43 | 17 | (-18) |

39 | 90 | 22 | 0 | (-2) |

30 | 49 | 28 | 0 | (-44) |

**Subtract column minima**

We subtract the column minimum from each column:

44 | 9 | 53 | 0 |

0 | 7 | 21 | 17 |

39 | 41 | 0 | 0 |

30 | 0 | 6 | 0 |

(-49) | (-22) |

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

There are 4 lines required to cover all zeros:

44 | 9 | 53 | 0 | x |

0 | 7 | 21 | 17 | x |

39 | 41 | 0 | 0 | x |

30 | 0 | 6 | 0 | x |

**The optimal assignment**

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

44 | 9 | 53 | 0 |

0 | 7 | 21 | 17 |

39 | 41 | 0 | 0 |

30 | 0 | 6 | 0 |

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

46 | 60 | 77 | 2 |

18 | 74 | 61 | 35 |

41 | 92 | 24 | 2 |

74 | 93 | 72 | 44 |

The optimal value equals 137.

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