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:

5 | 42 | 59 | 25 |

54 | 85 | 41 | 99 |

14 | 75 | 40 | 41 |

56 | 21 | 19 | 84 |

**Subtract row minima**

We subtract the row minimum from each row:

0 | 37 | 54 | 20 | (-5) |

13 | 44 | 0 | 58 | (-41) |

0 | 61 | 26 | 27 | (-14) |

37 | 2 | 0 | 65 | (-19) |

**Subtract column minima**

We subtract the column minimum from each column:

0 | 35 | 54 | 0 |

13 | 42 | 0 | 38 |

0 | 59 | 26 | 7 |

37 | 0 | 0 | 45 |

(-2) | (-20) |

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

There are 4 lines required to cover all zeros:

0 | 35 | 54 | 0 | x |

13 | 42 | 0 | 38 | x |

0 | 59 | 26 | 7 | x |

37 | 0 | 0 | 45 | x |

**The optimal assignment**

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

0 | 35 | 54 | 0 |

13 | 42 | 0 | 38 |

0 | 59 | 26 | 7 |

37 | 0 | 0 | 45 |

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

5 | 42 | 59 | 25 |

54 | 85 | 41 | 99 |

14 | 75 | 40 | 41 |

56 | 21 | 19 | 84 |

The optimal value equals 101.

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