# Transportation problem

### From Glossary

Find a flow of least cost that ships from supply sources to consumer destinations. This is a bipartite network, , where is the set of sources, is the set of destinations, and is the set of arcs. In the standard form, is bi-complete (A contains all arcs from to ), but in practice networks tend to be sparsely linked. Let be the unit cost of flow from to = supply at i-th source, and = demand at j-th destination. Then, the problem is the linear program:

The decision variables are called *flows*, and the two classes of constraints are called *supply limits* and *demand requirements*, resp. (Some authors use equality constraints, rather than than the inequalities shown.) An extension is the *capacitated transportation problem*, where the flows have bounds: