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:

26 | 30 | 82 | 76 |

56 | 16 | 33 | 86 |

81 | 26 | 47 | 18 |

39 | 52 | 35 | 58 |

**Subtract row minima**

We subtract the row minimum from each row:

0 | 4 | 56 | 50 | (-26) |

40 | 0 | 17 | 70 | (-16) |

63 | 8 | 29 | 0 | (-18) |

4 | 17 | 0 | 23 | (-35) |

**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 4 lines required to cover all zeros:

0 | 4 | 56 | 50 | x |

40 | 0 | 17 | 70 | x |

63 | 8 | 29 | 0 | x |

4 | 17 | 0 | 23 | x |

**The optimal assignment**

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

0 | 4 | 56 | 50 |

40 | 0 | 17 | 70 |

63 | 8 | 29 | 0 |

4 | 17 | 0 | 23 |

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

26 | 30 | 82 | 76 |

56 | 16 | 33 | 86 |

81 | 26 | 47 | 18 |

39 | 52 | 35 | 58 |

The optimal value equals 95.

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