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:

63 | 54 | 57 | 91 |

88 | 61 | 68 | 73 |

54 | 27 | 30 | 76 |

22 | 71 | 53 | 69 |

**Subtract row minima**

We subtract the row minimum from each row:

9 | 0 | 3 | 37 | (-54) |

27 | 0 | 7 | 12 | (-61) |

27 | 0 | 3 | 49 | (-27) |

0 | 49 | 31 | 47 | (-22) |

**Subtract column minima**

We subtract the column minimum from each column:

9 | 0 | 0 | 25 |

27 | 0 | 4 | 0 |

27 | 0 | 0 | 37 |

0 | 49 | 28 | 35 |

(-3) | (-12) |

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

There are 4 lines required to cover all zeros:

9 | 0 | 0 | 25 | x |

27 | 0 | 4 | 0 | x |

27 | 0 | 0 | 37 | x |

0 | 49 | 28 | 35 | x |

**The optimal assignment**

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

9 | 0 | 0 | 25 |

27 | 0 | 4 | 0 |

27 | 0 | 0 | 37 |

0 | 49 | 28 | 35 |

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

63 | 54 | 57 | 91 |

88 | 61 | 68 | 73 |

54 | 27 | 30 | 76 |

22 | 71 | 53 | 69 |

The optimal value equals 179.

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