A branch-and-cut algorithm for the windy profitable location rural postman problem

In this paper, we present an integer programming formulation for the windy profitable location rural postman problem (WPLRPP). We state and prove a theorem concerning the dimension of the associated polyhedron. Then, we use this theorem to study some trivial facets of the presented polyhedron. Furthermore, we adapt and validate several large families of valid inequalities for the WPLRPP. We also develop an efficient branch-and-cut algorithm for solving large WPLRPP instances, which leverages those inequalities. We compare our presented branch-and-cut algorithm with other efficient algorithms in the literature. The numerical results show that our algorithm solves larger problem instances and requires considerably less computing time than other algorithms in the literature.