Chapter 5 Arc routing methods and applications

Publisher Summary The term "arc routing" refers to routing problems where the key service activity is to cover arcs of a transportation network. In contrast to node routing, where the key service activity occurs at the nodes (customer sites) and arcs are of interest only as elements of paths that connect the nodes, arc routing focuses on the traversal of edges. Practical examples include the routing of street sweepers, snow-plowing, salt gritting (covering streets with salt grit), and inspection of streets for maintenance, postal delivery, and meter reading. In all examples, each street segment must be covered in its entirety. In meter reading, postal delivery, and the delivery of telephone books, the density of the customer locations along a street segment is sufficiently high to consider the street segment as a whole as the service entity. The basic methodology of arc routing by discussing generic arc routing models and their solution techniques is discussed. The chapter covers well-known postman problems that can be regarded as the classical problems of arc routing. The basic objective of these problems is to cover all arcs of a given network with an Euler cycle of minimum cost. The chapter considers the capacitated arc routing problem, where each vehicle tour (cycle) must observe an explicit capacity constraint. Two manufacturing problems that can be modeled as rural postman problems and also mentions other routing applications are discussed in the chapter.