A branch and cut approach for the mixed capacitated general routing problem

The issue addressed in this thesis consists in modeling and solving the Mixed Capacitated General Routing Problem (MCGRP). This problem generalizes many routing problems, either in the Node or in the Arc routing family. This makes the problem a very general one and gives it a big interest in realworld applications. Despite this, and because of the native di culty of the problem, very few papers have been devoted to this argument. In the thesis an integer programming model for the MCGRP is proposed and several valid inequalities for the undirected Capacitated Arc Routing polyhedron are extended and generalized to the MCGR polyhedron. A branch and cut algorithm for the MCGRP is developed and tested on a dataset of new instances derived from mixed CARP benchmark instances. Moreover an heuristic procedure is de ned in order to nd a good upper bound aimed at helping the branch and cut algorithm to cut o unpromising regions of the search tree. This schema will be used and extended in future works to solve bigger real-world instances. Extensive numerical experiments indicate that the algorithm is able to optimally solve many instances. In general, it provides valid lower and upper bounds for the problem in a reasonable amount of time.