  The Team Orienteering Problem (TOP) is an attractive variant of the Vehicle
Routing Problem (VRP). The aim is to select customers and at the same time
organize the visits for a vehicle fleet so as to maximize the collected profits
and subject to a travel time restriction on each vehicle. In this paper, we
investigate the effective use of a linear formulation with polynomial number of
variables to solve TOP. Cutting planes are the core components of our solving
algorithm. It is first used to solve smaller and intermediate models of the
original problem by considering fewer vehicles. Useful information are then
retrieved to solve larger models, and eventually reaching the original problem.
Relatively new and dedicated methods for TOP, such as identification of
irrelevant arcs and mandatory customers, clique and independent-set cuts based
on the incompatibilities, and profit/customer restriction on subsets of
vehicles, are introduced. We evaluated our algorithm on the standard benchmark
of TOP. The results show that the algorithm is competitive and is able to prove
the optimality for 12 instances previously unsolved.
