Routing Multiple Flows Through a Network

Abstract

Network flow models are some of the most frequently used tools for the planning of logistics systems because there exists a natural correspondence between the mathematical network flow formulation and the elements of the real-world supply chain network. The supply chain network consists of a number of suppliers that generate products transported over transportation channels through various intermediate facilities to a number of customers. Limiting capacities may exist on the transportation channels, the intermediate facilities, and capacity limitations on available goods at the suppliers may also exist. Demand satisfaction of the customers corresponds to a required outflow of products from the network. The mathematical network consists of nodes and arcs. The nodes can be further classified as sources that generate flow, intermediate nodes that neither generate nor consume flow, and destinations that consume flow. The nodes are connected by directional arcs. The arcs may have capacity limitations for individual flow types or jointly for all flows. A network flow schematic is illustrated in Fig. 7.1.