Q51188a Check whether the given transportation problem shown in Table No. 1 is a balanced one. If not, convert the unbalanced problem into a balanced transportation problem.

Source Destination Supply
1 2 3
1 25 45 10 200
2 30 65 15 100
3 15 40 55 400
Demand 200 100 300
Table No. 1 Transportation Model with Supply exceeding Demand

Solution:

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

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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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Thus, a dummy destination is added to the table, with a demand of 100 units. The modified table is shown in Table 2 which has been converted into a balanced transportation table. The unit costs of transportation of dummy destinations are assigned as zero.

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Table No. 2 Dummy Destination Added
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