Approximations for many-visits multiple traveling salesman problems

A fundamental variant of the classical traveling salesman problem (TSP) is so-called multiple TSP (mTSP), where a set m salesmen jointly visit all cities from 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 variety heuristic and exact solution procedures that solve instances. In this work we consider further generalization mTSP, many-visits each city v has request r(v) how times it should be visited salesmen. This opens up new applications such as aircraft sequencing, while at same time poses several computational challenges. We provide polynomial-time algorithms variants compute constant-factor approximate solutions.