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:

95 | 59 | 59 | 93 |

82 | 95 | 55 | 17 |

17 | 85 | 21 | 74 |

99 | 46 | 9 | 29 |

**Subtract row minima**

We subtract the row minimum from each row:

36 | 0 | 0 | 34 | (-59) |

65 | 78 | 38 | 0 | (-17) |

0 | 68 | 4 | 57 | (-17) |

90 | 37 | 0 | 20 | (-9) |

**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:

36 | 0 | 0 | 34 | x |

65 | 78 | 38 | 0 | x |

0 | 68 | 4 | 57 | x |

90 | 37 | 0 | 20 | x |

**The optimal assignment**

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

36 | 0 | 0 | 34 |

65 | 78 | 38 | 0 |

0 | 68 | 4 | 57 |

90 | 37 | 0 | 20 |

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

95 | 59 | 59 | 93 |

82 | 95 | 55 | 17 |

17 | 85 | 21 | 74 |

99 | 46 | 9 | 29 |

The optimal value equals 102.

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