I was reading Balanced transportation problem. I got stuck in the conditions of Basic Feasible solution.
If we suppose a transportation problem where $m$ number of supply points and $n$ number of demand points then why the basic feasible solution always involves not more than $m+n-1$ allocations.
My confusion — If we consider this transportation problem as L.P.P problem then it will have $m+n$ equations and $mn$ variable. So we can get $m+n$ basic variable. i.e there can be $m+n$ allocation .
But it does not happen. Whenever we see there is $m+n$ allocations we can be confident that there is a loop.
Can anyone please help me to understand where I am missunderstanding?
Can anyone please help me ?
Best Answer
The transportation problem only has $m+n-1$ independent constraints, see this answer. That means that there cannot be $m+n$ basic variables, but only $n+m-1$.