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:

68 | 61 | 91 | 10 |

86 | 90 | 70 | 78 |

76 | 94 | 52 | 87 |

77 | 33 | 77 | 76 |

**Subtract row minima**

We subtract the row minimum from each row:

58 | 51 | 81 | 0 | (-10) |

16 | 20 | 0 | 8 | (-70) |

24 | 42 | 0 | 35 | (-52) |

44 | 0 | 44 | 43 | (-33) |

**Subtract column minima**

We subtract the column minimum from each column:

42 | 51 | 81 | 0 |

0 | 20 | 0 | 8 |

8 | 42 | 0 | 35 |

28 | 0 | 44 | 43 |

(-16) |

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

There are 4 lines required to cover all zeros:

42 | 51 | 81 | 0 | x |

0 | 20 | 0 | 8 | x |

8 | 42 | 0 | 35 | x |

28 | 0 | 44 | 43 | x |

**The optimal assignment**

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

42 | 51 | 81 | 0 |

0 | 20 | 0 | 8 |

8 | 42 | 0 | 35 |

28 | 0 | 44 | 43 |

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

68 | 61 | 91 | 10 |

86 | 90 | 70 | 78 |

76 | 94 | 52 | 87 |

77 | 33 | 77 | 76 |

The optimal value equals 181.

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