UNBALANCED TRANSPORTATION PROBLEM - Quantitative Techniques for management

Unbalanced transportation problem in Operational Research

When the total supply of all the sources is not equal to the total demand of all destinations, the problem is an unbalanced transportation problem.

Total supply ≠ Total demand

unbalanced transportation problem

Demand Less than Supply

In real-life, supply and demand requirements will rarely be equal. This is because of variation in production from the supplier end, and variations in forecast from the customer end. Supply variations may be because of shortage of raw materials, labour problems, Transportation Model improper planning and scheduling. Demand variations may be because of change in customer preference, change in prices and introduction of new products by competitors.

These unbalanced problems can be easily solved by introducing dummy sources and dummy destinations. If the total supply is greater than the total demand, a dummy destination (dummy column) with demand equal to the supply surplus is added. If the total demand is greater than the total supply, a dummy source (dummy row) with supply equal to the demand surplus is added. The unit transportation cost for the dummy column and dummy row are assigned zero values, because no shipment is actually made in case of a dummy source and dummy destination.

Example : Check whether the given transportation problem shown in Table is a balanced one. If not, convert the unbalanced problem into a balanced transportation problem.

Transportation Model with Supply Exceeding Demand

Transportation Model with Supply Exceeding Demand

Solution: For the given problem, the total supply is not equal to the total demand.

total supply is not equal to the total demand.

The given problem is an unbalanced transportation problem. To convert the unbalanced transportation problem into a balanced problem, add a dummy destination (dummy column). i.e., the demand of the dummy destination is equal to,

demand of the dummy destination

Thus, a dummy destination is added to the table, with a demand of 100 units. The modified table is shown in Table which has been converted into a balanced transportation table. The unit costs of transportation of dummy destinations are assigned as zero.

Dummy Destination Added

Dummy Destination Added

Similarly,

Dummy Destination Added

Demand Greater than Supply

Example : Convert the transportation problem shown in Table into a balanced problem.

Demand Exceeding Supply

Demand Exceeding Supply

Solution: The given problem is,

Demand Exceeding Supply

The given problem is an unbalanced one. To convert it into a balanced transportation problem, include a dummy source (dummy row) as shown in Table

Balanced TP Model

Balanced TP Model


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