What is Looping in a Transportation problem?

Looping in a Transportation problem.  (Apr 2004)

In transportation problem we get a loop when solution is not optimal. We find delta value (opportunity cost) for each unoccupied cell. Delta = C – (U + V). If any delta is negative, solution is not optimal. In next table there is scope for reducing the cost. Hence, we draw a loop from maximum negative delta. The loop can be a four corner loop or a six corner loop.

Signs at the corner of the loop are: positive (+) sign at starting point and then alternate negative (-) and positive (+) sign at other corners. From this we get new values for the next transportation matrix. Only values at the corner of the loop change. Other values in the matrix remain same.