Transportation Problem

Prohibited Routes

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 µ 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

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

Factory	Warehouse			Supply
	W1	W2	W3
F1		µ		200
F2			18	160
F3		µ	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.