As mentioned in the previous chapter, there are four main types of linear programming structures, three of which we covered in that chapter. The fourth type is the network model, which is the subject of this chapter. Network models themselves fall into several categories, but what is common in our approach to all network models is that we use a diagram to help formulate and solve linear programming problems.
The network model describes patterns of flow in a connected system, where the flow might involve material, people, or funds. The system elements may be locations, such as cities, warehouses, or assembly lines; or they may be points in time rather than points in space. When we construct diagrams to represent such systems, the elements are represented by nodes, or circles, in the diagram. The paths of flow are represented by arcs, or arrows. Figure 10.1 shows a very simple diagram, in which the network elements are a factory (node 1) and two warehouses (nodes 2 and 3). The arc from node 1 to node 2 carries the flow (truckloads of goods, perhaps) from the factory to the first warehouse; similarly, the arc from node 1 to node 3 carries the flow from the factory to the second warehouse.
As we shall see, drawing a network diagram helps us formulate an appropriate linear programming model, and if we encounter difficulties in getting our model to work, the diagram can also be a helpful device for troubleshooting.