Page 131 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Conditions for Forming a Loop
1. The start and end points of a loop must be the same.
2. The lines connecting the cells must be horizontal and vertical.
3. The turns must be taken at occupied cells only.
4. Take a shortest path possible (for easy calculations).

Notes

1. Every loop has an even number of cells and at least four cells.
2. Each row or column should have only one ‘+’ and ‘-‘ sign.
3. Closed loop may or may not be square in shape. It can also be a rectangle or a
stepped shape.
4. It doesn’t matter whether the loop is traced in a clockwise or anti-clockwise direction.
Take the most negative '– q' value, and shift the allocated cells accordingly by adding the
value in positive cells and subtracting it in the negative cells. This gives a new improved
table. Then go to step 5 to test for optimality.

Calculate the Total Transportation Cost

Since all the C values are positive, optimality is reached and hence the present allocations are
ij
the optimum allocations. Calculate the total transportation cost by summing the product of
allocated units and unit costs.

Task Find the initial basic solution for the transportation problem and hence solve it.
Destination
Source Supply
1 2 3 4
1 4 2 7 3 250
2 3 7 5 8 450
3 9 4 3 1 500
Demand 200 400 300 300 1200

6.5 Prohibited Routes Problem

In practice, there may be routes that are unavailable to transport units from one source to one or
more destinations. The problem is said to have an unacceptable or prohibited route. To overcome
such kind of transportation problems, assign a very high cost to prohibited routes, thus preventing
them from being used in the optimal solution regarding allocation of units.

6.6 Transshipment Problem

The transshipment problem is an extension of the transportation problem in which the commodity
can be transported to a particular destination through one or more intermediate or transshipment
nodes.

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