# Prohibited Routes: Transportation Problem

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.

## Example: Prohibited Transportation Problem

Consider the following transportation problem.

Factory Warehouse Supply
W1 W2 W3
F1 16 12 200
F2 14 8 18 160
F3 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

Use Horizontal Scrollbar to View Full Table Calculation.

Factory Warehouse Supply
W1 W2 W3
F1 200
F2 18 160
F3 16 90
Demand 180 120 150 450
##### Initial basic feasible solution

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

The minimum transportation cost is Rs. 6460.

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