Ricardo Fukasawa The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. … Read more
In recent years there has been growing interest in generating valid inequalities for mixed-integer programs using sets with 2 or more constraints. In particular, Andersen et.al (2007) and Borozan and Cornue’jols (2007) study sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes … Read more
The master equality polyhedron (MEP) is a canonical set that generalizes the Master Cyclic Group Polyhedron (MCGP) of Gomory. We recently characterized a nontrivial polar for the MEP, i.e., a polyhedron T such that an inequality denotes a nontrivial facet of the MEP if and only if its coefficient vector forms a vertex of T. … Read more
We study the Master Equality Polyhedron (MEP) which generalizes the Master Cyclic Group Polyhedron and the Master Knapsack Polyhedron. We present an explicit characterization of the polar of the nontrivial facet-defining inequalities for the MEP. This result generalizes similar results for the Master Cyclic Group Polyhedron by Gomory (1969) and for the Master Knapsack Polyhedron … Read more
This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to $q$-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence probem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. … Read more