Sometimes there may be situations, where it is not possible
to use certain routes in a **transportation problem**. For example, road
construction, bad road conditions, strike, unexpected floods, local
traffic rules, etc.

We can handle such type of problems in different ways:

- A very large cost represented by M or ∞ is assigned to each of such routes, which are not available.
- To block the allocation to a cell with a prohibited route, we can cross out that cell.

The problem can then be solved in its usual way.

Consider the following transportation problem.

Factory | Warehouse | Supply | ||
---|---|---|---|---|

W_{1} |
W_{2} |
W_{3} |
||

F_{1} |
16 | ∞ | 12 | 200 |

F_{2} |
14 | 8 | 18 | 160 |

F_{3} |
26 | ∞ | 16 | 90 |

Demand | 180 | 120 | 150 | 450 |

Solution.

An initial solution is obtained by the matrix minimum method and is shown in the final table.

Final Table

Factory | Warehouse | Supply | ||
---|---|---|---|---|

W_{1} |
W_{2} |
W_{3} |
||

F_{1} |
∞ | |||

F_{2} |
18 | |||

F_{3} |
∞ | 16 | ||

Demand | 450 |

16 X 50 + 12 X 150 + 14 X 40 + 8 X 120 + 26 X 90 = 6460.

The minimum transportation cost is Rs. 6460.