Search results for "Polyhedral analysis"
showing 2 items of 2 documents
The Windy clustered prize-collecting arc-routing problem
2011
This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. A mathematical programming formulation is given and some polyhedral results including several facet-defining and valid inequalities are presented. The separation problem for the different families of inequalities is studied. Numerical results from computational experiments are analyzed. © 2011 INFORMS.
The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm
2017
[EN] The Hierarchical Mixed Rural Postman Problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters' that have to be serviced in a hierarchical order. The problem generalizes the Mixed Rural Postman Problem and thus is NP-hard. In this paper, we provide a polyhedral analysis of the problem and propose a branch-and-cut algorithm for its solution based on the introduced classes of valid inequalities. Extensive computational experiments are reported on benchmark instances. The exact approach allows to find the optimal solutions in less than 1 hour for instances with up to 999 vertices, 2678 links, and five clusters.