lowest cost entry method s lcem or matrix minima

Question

Lowest Cost Entry method s( LCEM) or Matrix Minima Method:

Step1: Determine  the smallest  cost in  the cost matrix of the transportation table. Let it be ( C_ij). Allocate S_ij = min (a _i , b _j) in the cell( i, j).

Step 2:

a. If X_ij = a_i cross  out the  i row of the  transportation  table  and decrease b by a_j. Go to steps3.

b. If X_ij = b cross out the  j column of the transportation  table and decrease a_i by b_j go to step 3.

c.  If X_ij = a_i = b_j cross out  either the  row or j column but not both .

Step 3: Te peat steps  1 and 2  for the resulting reduced transportation  table until  all the  requirements  are satisfied. Whenever the minimum   cost is  not unique make an  arbitrary choice among  the minims.