  A fundamental variant of the classical traveling salesman problem (TSP) is
the so-called multiple TSP (mTSP), where a set of $m$ salesmen jointly visit
all cities from a set of $n$ cities. The mTSP models many important real-life
applications, in particular for vehicle routing problems. An extensive survey
by Bektas (Omega 34(3), 2006) lists a variety of heuristic and exact solution
procedures for the mTSP, which quickly solve particular problem instances.
  In this work we consider a further generalization of mTSP, the many-visits
mTSP, where each city $v$ has a request $r(v)$ of how many times it should be
visited by the salesmen. This problem opens up new real-life applications such
as aircraft sequencing, while at the same time it poses several computational
challenges. We provide multiple efficient approximation algorithms for
important variants of the many-visits mTSP, which are guaranteed to quickly
compute high-quality solutions for all problem instances.
