Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut-and-Price algorithm yielding provably good solutions for instances with vertical bar V vertical bar <= 3795. Key ingredients of the algorithm are a delayed column-and-row generation technique, exploiting the special structure of the formulation, to solve the LP-relaxation, and cutting planes to strengthen the formulation and limit the size of the enumeration tree
Given a simple graph G(V, E) and a set of traffic demands between the nodes of G, the Network Loading Problem consists of installing minimum cost integer capacities on the edges of G allowing routing of traffic demands. In this paper we study the Capacity Formulation of the Network Loading Problem, introducing the new class of Tight Metric Inequalities, that completely characterize the convex hull of the integer feasible solutions of the problem. We present separation algorithms for Tight Metric Inequalities and a cutting plane algorithm, reporting on computational experience. (c) 2006 Elsevier B.V. All rights reserved
The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs of a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are of a Branch-and-Price type, with lower bounds computed through Dantzig-Wolfe reformulation and column generation.In this paper we propose a cutting plane algorithm working in the space of the variables of the basic formulation, whose core is an exact separation procedure for the knapsack polytopes induced by the capacity constraints. We show that an efficient implementation of the exact separation procedure allows to deal with large-scale instances and to solve to optimality several previously unsolved instances.
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