We introduce a novel incremental network design problem motivated by the expansion of hub capacities in package express service networks: the \textit{incremental network design problem with multi-commodity flows}. We are given an initial and a target service network design, defined by a set of nodes, arcs, and origin-destination demands (commodities), and we seek to find … Read more
In 2013, Orlin proved that the max flow problem could be solved in O(nm) time. His algorithm was the fastest for very sparse graphs. If the graph was not sufficiently sparse, the fastest running time was an algorithm due to King, Rao, and Tarjan. We describe a new variant of the excess scaling algorithm for … Read more
In this paper, we propose new constraint generation algorithms for solving the two-stage robust minimum cost flow problem, a problem that arises from various applications such as transportation and logistics. In order to develop efficient algorithms under general polyhedral uncertainty set, we repeatedly exploit the network-flow structure to reformulate the two-stage robust minimum cost flow … Read more
We discuss interior point methods for large-scale linear programming, with an emphasis on methods that are useful for problems arising in telecommunications. We give the basic framework of a primal-dual interior point method, and consider the numerical issues involved in calculating the search direction in each iteration, including the use of factorization methods and/or preconditioned … Read more
We describe FORTRAN subroutines for network flow optimization using an interior point network flow algorithm. We provide FORTRAN and C language drivers, as well as C language functions that, together with the subroutines, make up PDNET (Portugal, Resende, Veiga, and Júdice, 2000). The algorithm is described in detail and its implementation is outlined. Usage of … Read more
We study capacitated network flow problems with supplies and demands defined on a countably infinite collection of nodes having finite degree. This class of network flow models includes, for example, all infinite horizon deterministic dynamic programs with finite action sets since these are equivalent to the problem of finding a shortest infinite path in an … Read more
We study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners are tested using PDNET, a state-of-the-art interior point code for the minimum cost network flow problem. … Read more