Approximate solutions of capacitated fixed‐charge minimum cost network flow problems

Abstract

AbstractThis article proposes two approximate methods to solve capacitated, single‐commodity and fixed‐charge network flow problems. First, relaxed problems obtained by the Lagrange relaxation method are shown to form a minimum spanning tree problem, yielding a lower bound to the original problem. The subgradient optimization technique can be then applied to improve this bound by updating the Lagrange multipliers. The second part of the article presents a new, simple, and efficient heuristic to find a feasible and approximate solution that is also an upper bound to the original problem.