Page 130 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 6: Transportation Problem – Optimality Tests

Notes
If C values are > 0 then, the basic initial feasible solution is optimal.
ij
If C values are = 0 then, the multiple basic initial feasible solution exists.
ij
If C values are < 0 then, the basic initial feasible solution is not optimal.
ij

Notes The MODI method is based on the concept of Duality.

Did u know? MODI method is also known as u-v method or method of multipliers.
6.4 Procedure for Shifting of Allocations

Select the cell which has the most negative C value and introduce a positive quantity called ‘’
ij
in that cell. To balance that row, allocate a ‘– ’ to that row in occupied cell. Again, to balance that
column put a positive ‘’ in an occupied cell and similarly a ‘–’ to that row. Connecting all the
‘’s and ‘–‘s, a closed loop is formed.
Two cases are represented in Table 6.1 (a) and 6.1 (b). In Table 6.1 (a) if all the  allocations are
joined by horizontal and vertical lines, a closed loop is obtained.
The set of cells forming a closed loop is

CL = {(A, 1), (A, 3), (C, 3), (C, 4), (E, 4), (E, 1), (A, 1)}
The loop in Table 4.22(b) is not allowed because the cell (D3) appears twice.
Table 6.1(a)

1 2 3 4
A
B

C
D

E

Table 6.1(b)

1 2 3 4
A

B
C
D

E

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