  In this work, we introduce a generalization of the well-known Vehicle Routing
Problem for a specific application in the monitoring of a Water Distribution
Network (WDN). In this problem, multiple technicians must visit a sequence of
nodes in the WDN and perform a series of tests to check the quality of water.
Some special nodes (i.e., wells) require technicians to first collect a key
from a key center. The key must then be returned to the same key center after
the test has been performed, thus introducing precedence constraints and
multiple visits in the routes. To solve the problem, three mathematical models
and an Iterated Local Search have been implemented. The efficiency of the
proposed methods is demonstrated by means of extensive computational tests on
randomly created instances, as well as on instances derived from a real-world
case study.
