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- Thomas L. Magnanti, Richard T. Wong
- Operations Research
- 1981

- Thomas L. Magnanti, Prakash Mirchandani, Rita Vachani
- Math. Program.
- 1993

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to… (More)

- Thomas L. Magnanti, Richard T. Wong
- Transportation Science
- 1984

- Anantaram Balakrishnan, Thomas L. Magnanti, Richard T. Wong
- Operations Research
- 1989

The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling. We develop a family of dual ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location, Steiner network and directed spanning tree problems.… (More)

- Thomas L. Magnanti, Prakash Mirchandani, Rita Vachani
- Operations Research
- 1995

- Luís Gouveia, Thomas L. Magnanti
- Networks
- 2003

The Diameter-Constrained Minimum Spanning Tree Problem seeks a least cost spanning tree subject to a (diameter) bound imposed on the number of edges in the tree between any node pair. A traditional multicommodity flow model with a commodity for every pair of nodes was unable to solve a 20-node and 100-edge problem after one week of computation. We formulate… (More)

- Keely L. Croxton, Bernard Gendron, Thomas L. Magnanti
- Management Science
- 2003

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

- Anantaram Balakrishnan, Thomas L. Magnanti, Prakash Mirchandani, Anantaram Balakrishnant

Given an undirected network with L possible facility types for each edge, and a partition of the nodes into L levels, the Multi-level Network Design (MLND) problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher type. This problem generalizes the well-known… (More)