costing query- transportation

werever u place d e,it shd nt form a rectangular or square loop in d intial BFS..

As per my knowledge Independent cell represents
 

a) an unallocated cell and

b) a cell which should fall in the regular row or column i.e, it should not fall in the dummy row or  column if inserted.

Please let me know if i am correct

both these conditions are satisfied. however i still don't understand what bhumika means by forming a loop. i have given the IBFS below. allocation is as follows- 

row 1- columns 2,4,5

row 2 - column 1

row 3- column 3

row 4- column 1 & 4

 now can u explain why '5' ( row 4 column 3) is chosen to allocate 'e' and not '3' (row 4 column 2)

as bhumika rightly said, independent cell means it should not form a loop with the allocated cell. the cell which has least cost of 3 forms a loop with row 1 colum 2 and column 4 and row 4 column 4 whereas the next least cost 5 is unable to form any loop whatsoever, hence 5 is selected

Mallika's and bhumika's answer is right and perfect......

BY USING '3', WE ARE ABLE TO MAKE A LOOP, BUT FROM THE NEXT LEAST NO. I.E. '5', LOOP CAN'T BE MADE, SO WE WILL PUT 'e' TO IT........

AND 'e' JUST MEANS 0... i.e. allocate 0 units to that cell to satisfy the equation 'm+n-1'.,.............

When allocating u and v values for the matrix u+v=Cij for allocated cells, it is not possible to allocate u & v values for column 3 & row3

e is to be allocated to the least cost unallocated cell in this column 3 & row3

evenif 3 is the least cost unallocated cell in the matrix, it is not in this column3 or row3

Therefore 5 is selected- which is in the column 3

 ok got it now. thanks a lot everyone.

Hey one question. how is loop formed.. is it formed using the already located cell.

i think d final allocation will be same even if u choose least cost independent cell as 3' (row 4 column 2)

Hey guys so if this is the initial basic solution can we insert 'e' in any of the 400 cell(i.e; row 1 column 2 or row 3 column 3)? The cells in colour are the allocated cells.

If we are not able to create a loop in R4C3 then we are not avle to creare a loop in R4C2 also hence answer by christina is perfect