We consider a network consists of five nodes and a set of arcs. There are two supply nodes (1 and 2) and two demand nodes (4 and 5). Note 3 is a transshipment node.

graph LR;
    1((1))-->2;
    1-->3;
    1-->4;
    2((2))-->3;
    3((3))-->5;
    5((5))-->4;
    4((4))-->5;

(Unfortunately GitHub do not support the visualization of mermaid graphs not yet (github/markup#533). But you can view on VS Code.)

In the input file are the given informations

• costs per unit flow through the arcs,
• maximal capacities for the arcs,
• net flow generated at the nodes.

The aim is to minimize the total costs of sending the available supply through the network to satisfy the demand.