row minima methodssteps1 the smallest cost in

Question

Row Minima Methods:

Steps1: The smallest cost  in the first  row  of the  transportation table  is determined. Let it be C_1j  . allocate as much  as possible amount X_1j = min (a₁ ,b₁) so that either the  capacity  of  origin  O₁ is exhausted  or the requirement at destination D j is satisfied or both .

Steps2:

a. If X₁ = a₁ so  that the  availability at  origin O₁ is completely exhausted cross out the first  row  of the table  and move  down  to the second  row.

b. If X₁ = a₁ b₁ the origin capacity a1 is completely exhausted as well  as the requirement at  destination D_j is completely  satisfied. An arbitrary tie breaking choice is made. Cross out  the j column and make the second allocation  X_1k = 0  in the cell ( 1k ) with C1k  being  the new  minimum  cost  in the first  row. Cross  out the  first  row  and move  down  to the second row.

c.  If X₁j= b_j so that the requirement at destination Dj  is satisfied cross out the j  column and reconsider the first  row  with the  remaining availability  of origin O₁.

Step 3: Repeat steps  I and 2 for the reduced transportation table  until all the  requirements  are satisfied.