The problem is to determine an optimum shipping plan that minimizes the total cost of shipping while meeting all customer demands with available supplies. Arc lower bounds 0 and upper bound 200. This problem is ready made for a network flow model, and we use it to describe the several components of this model type. The network model is graphical in that it is presented as a collection of the nodes and arcs drawn in the figure. The nodes represent the cities of this problem, and we name them with the shortened names of the supply and demand cities.
Arcs are the directed line segments of the figure.
The nodes at its ends identify an arc. One arc in the figure originates at node Phoenix and terminates at node Chicago. Flow is associated with the network, entering and leaving at the nodes and passing through the arcs. Flows entering or leaving a node from external sources are called external flows and are shown adjacent to the nodes in the square brackets. A positive external flow is a supply, flow that enters the network, and a negative external flow is a demand, flow that leaves the network.