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:

79 | 3 | 96 | 22 |

48 | 37 | 39 | 19 |

22 | 56 | 38 | 38 |

75 | 57 | 71 | 93 |

**Subtract row minima**

We subtract the row minimum from each row:

76 | 0 | 93 | 19 | (-3) |

29 | 18 | 20 | 0 | (-19) |

0 | 34 | 16 | 16 | (-22) |

18 | 0 | 14 | 36 | (-57) |

**Subtract column minima**

We subtract the column minimum from each column:

76 | 0 | 79 | 19 |

29 | 18 | 6 | 0 |

0 | 34 | 2 | 16 |

18 | 0 | 0 | 36 |

(-14) |

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

There are 4 lines required to cover all zeros:

76 | 0 | 79 | 19 | x |

29 | 18 | 6 | 0 | x |

0 | 34 | 2 | 16 | x |

18 | 0 | 0 | 36 | x |

**The optimal assignment**

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

76 | 0 | 79 | 19 |

29 | 18 | 6 | 0 |

0 | 34 | 2 | 16 |

18 | 0 | 0 | 36 |

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

79 | 3 | 96 | 22 |

48 | 37 | 39 | 19 |

22 | 56 | 38 | 38 |

75 | 57 | 71 | 93 |

The optimal value equals 115.

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