New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem

Abstract

AbstractThe min–max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch‐and‐cut algorithm that produced some promising computational results was implemented. In this article, we present further results for this problem. We describe several new facet‐inducing inequalities obtained from the WRPP, as well as some inequalities that have to be satisfied by any optimal solution. We present an enhanced branch‐and‐cut algorithm that takes advantage of both these new inequalities and high quality min–max K‐WRPP feasible solutions obtained by a metaheuristic. Computational results on a large set of instances are also reported. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 255–272 2011