A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design

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. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints show that the dual-ascent procedure and an associated drop-add heuristic generate solutions that, in almost all cases, are guaranteed to be within 1 to 4% of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks, including some models that arise in freight transport.