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- 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, Prakash Mirchandani, Rita Vachani
- Operations Research
- 1995

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

- Thomas L. Magnanti, Prakash Mirchandani
- Networks
- 1993

- 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.

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

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

This paper studies a multi-facility network synthesis problem, called the Two-level Network Design (TLND) problem, that arises in the topological design of hierarchical communication, transportation, and electric power distribution networks. The nodes of a multi-level network have varying levels of importance; more critical or higher level nodes require… (More)

- Yuping Qiu, Thomas L. Magnanti
- Math. Oper. Res.
- 1989

Variational inequalities have often been used as a mathematical programming tool in modeling various equilibria in economics and transportation science. The behavior of such equilibrium solutions as a result of the changes in problem data is always of concern. In this paper, we present an approach for conducting sensitivity analysis of variational… (More)

- 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)