Special cases in transportation models

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21/8/2017

SPECIAL CASES IN TRANSPORTATION MODELS More than one optimal solution Happens when there exists zero improvement index at the last table.

Degeneracy Happens when No. of used squares < no. of rows + no. of columns – 1 Add an artificial zero to an unused square and treat the square as a used square

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21/8/2017

1. Degeneracy happens because both supply and demand are satisfied simultaneously. To

3. Add artificial zero at one of these squares. Usually, the square with the lowest cost is chosen.

W

From

X

Y

Supply

6

0

3

8

200

U

4

300

9

2

300

V

3

400

8

100

5

500 100

700 400

100

T

200

Demand

200

2. Instead of moving to the right or down, one has to move diagonally to go to the next square.

4. After adding artificial zero, continue solving the problem as usual.

SECOND TABLE

To

W

From

T

6 8

U V Demand

X

200

4

3 0

+

200

Y

200

3

100

9

400

8

700

Supply 8

200

2

300

5

500

8 ‐4 +

100

100

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21/8/2017

THIRD TABLE 1. Degeneracy happens because two values vanish simultaneously. To From

W 6

T U

200

200

4 3

V Demand

X

200

2. Add artificial zero at one of the squares. Usually, the square with the lowest cost is chosen.

500 700

Y 3

Supply 8

200

9

100

2

300

8

0

5

500

100 3. After adding artificial zero, continue solving the problem as usual.

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