In network modelling LP , when Supply < Demand and we use normal balance of flow rule for all the constraints, i.e.
(inflow - outflow) <= supply or demand,
we say we are trying to redistribute the available resources at the least cost possible.
However, when we add a dummy node with infinite supply and infinitely expensive supply route to all the demand nodes, we are able to reverse the balance of flow rule:
(inflow - outflow) >= supply or demand.
After solving, the artificial decision variables values are ignored and the rest add up to being the required solution.
Now, we say that we're trying to meet as much demand as possible at the least cost.
I fail to understand the difference. In cases where,
inflow into a node = the outflow from the node, the difference solutions from the two approaches don't make any sense at all. Given that we don't change the original problem, the second approach generally increases the cost through the route. How is that of any value to us?
It does make a little sense when the efficiency of the nodes are different though, i.e.,
inflow into a node > outflow from the node (generally a percent of the raw materials coming in).
