Minimizes the cost of shipping a single commodity from supply points to demand points, given a per-unit shipping cost for every supply-demand pair.
Subject to:
- for every supply point (supply capacity)
- for every demand point (demand requirement)
Balanced Transportation Problem
Total supply equals total demand: . Every constraint becomes an equality.
Necessary and Sufficient Condition for Feasibility
A feasible solution exists iff the problem is balanced.
Unbalanced Transportation Problem
Total supply and demand differ. Add a dummy supply point (if demand exceeds supply) or a dummy demand point (if supply exceeds demand) with 0 shipping cost, absorbing the excess, to rebalance it.
Maximization Transportation Problem
Convert to an equivalent minimization problem by negating every cost (or subtracting each from the largest cost in the matrix), then solve as usual.
Restricted Transportation Problem
A route is prohibited (e.g. no road between a supply and demand point). Assign it a very large cost , which drives to 0 in any optimal solution.