A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure

Abstract

In this paper, we consider the Fixed Charge Network Flow Problem (FCNFP) which is known to be NP -hard. It has many practical applications including transportation, network design, communication, and production scheduling. Although many exact methods have been developed to solve the FCNFP, their computational requirements increase exponentially with the size of the problem. Hence, heuristic approaches are needed to solve suboptimally large-scale problems. Here, we propose a new approach for solving the general capacitated (or uncapacitated) FCNFP by adapting an economic viewpoint of the fixed cost. A new concept of the dynamic slope scaling procedure is presented and some computational results on a wide range of test problems are reported. The largest problem has 202 nodes and 10 200 arcs. The results show that the proposed procedure generates solutions within 0% to 0.65% of optimality in all cases.