In the previous section, the number of persons and the number of jobs
were assumed to be the same. In this section, we remove this assumption
and consider a situation where the **number of persons is not equal to
the number of jobs**. In all such cases, fictitious rows and/or columns
are added in the matrix to make it a square matrix.

Then, we apply the
usual Hungarian algorithm to this resulting balanced assignment problem.
We provide the following example to illustrate the solution of an **unbalanced
assignment problem**.
## Example: Unbalanced Assignment Problem

Job | ||||
---|---|---|---|---|

Person | 1 | 2 | 3 | 4 |

A | 20 | 25 | 22 | 28 |

B | 15 | 18 | 23 | 17 |

C | 19 | 17 | 21 | 24 |

Solution

Since the number of persons is less than the number of jobs, we introduce a dummy person (D) with zero values. The revised assignment problem is given below:

Table

Job | ||||
---|---|---|---|---|

Person | 1 | 2 | 3 | 4 |

A | 20 | 25 | 22 | 28 |

B | 15 | 18 | 23 | 17 |

C | 19 | 17 | 21 | 24 |

D (dummy) | 0 | 0 | 0 | 0 |

Now use the Hungarian method to obtain the optimal solution yourself.

Ans. = 20 + 17 + 17 + 0 = 54.