Page 111 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Total supply  Total demand

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5.6.1 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, 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 5.9 is a balanced one. If not,
convert the unbalanced problem into a balanced transportation problem.

Table 5.9: Transportation Model with Supply exceeding Demand

Destination
Source Supply
1 2 3
1 25 45 10 200
2 30 65 15 100
3 15 40 55 400
Demand 200 100 300

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

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since,

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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,

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