The General Routing Problem (GRP) is the problem of finding a minimum cost
route for a single vehicle, subject to the condition that the vehicle visit
s certain vertices and edges of a network. It contains the Rural Postman Pr
oblem, Chinese Postman Problem and Graphical Travelling Salesman Problem as
special cases. We describe a cutting plane algorithm for the GRP based on
facet-inducing inequalities and show that it is capable of providing very s
trong lower bounds and, in most cases, optimal solutions.