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.

Solution.

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

Final Table

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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.