Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
Integer and combinatorial optimization
Integer and combinatorial optimization
A branch-and-bound method for the fixed charge transportation problem
Management Science
Minimum concave-cost network flow problems: applications, complexity, and algorithms
Annals of Operations Research
Revised-modified penalties for fixed charge transportation problems
Management Science
A Dynamic Domain Contraction Algorithm for Nonconvex Piecewise Linear Network Flow Problems
Journal of Global Optimization
Parallel Computing - Special issue: Parallel computing in logistics
On network design problems: fixed cost flows and the covering steiner problem
ACM Transactions on Algorithms (TALG)
A Branch-and-Bound Algorithm for Concave Network Flow Problems
Journal of Global Optimization
Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems
Journal of Global Optimization
Dynamic Slope Scaling Procedure and Lagrangian Relaxation with Subproblem Approximation
Journal of Global Optimization
Adaptive dynamic cost updating procedure for solving fixed charge network flow problems
Computational Optimization and Applications
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Large-Scale, Less-than-Truckload Service Network Design
Operations Research
Combining Exact and Heuristic Approaches for the Capacitated Fixed-Charge Network Flow Problem
INFORMS Journal on Computing
A heuristic method for the minimum toll booth problem
Journal of Global Optimization
Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm
Computers and Industrial Engineering
Journal of Combinatorial Optimization
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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 10200 arcs. The results show that the proposed procedure generates solutions within 0% to 0.65% of optimality in all cases.