Optimum synthesis of discrete capacitated networks with multi-terminal commodity flow requirements

Network design problems arise in a wide range of applied areas including telecommunications, computer networks, and transportation. In this paper, we address the following discrete capacitated multi-terminal network design problem. Given a connected digraph G = (V,A), a set of L potential facilities to be installed on each arc, and a set of K multi-terminal (non-simultaneous) commodity flow requirements, the problem is to find a set of facilities to install in order to route the K nonsimultaneous flows while minimizing the total fixed plus variable costs. We describe an exact procedure for solving this problem based on Benders decomposition. Our algorithm includes several features that significantly improve the efficiency of the basic approach. Computational results attest to the efficacy of the proposed algorithm, which can solve medium- to large-scale problems to optimality.

[1]  Antonino Maugeri,et al.  Equilibrium problems and variational models , 2003 .

[2]  Michel Minoux,et al.  Networks synthesis and optimum network design problems: Models, solution methods and applications , 1989, Networks.

[3]  Katta G. Murty,et al.  Solving the Fixed Charge Problem by Ranking the Extreme Points , 1968, Oper. Res..

[4]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[5]  John N. Hooker,et al.  Solving Fixed-Charge Network Flow Problems with a Hybrid Optimization and Constraint Programming Approach , 2002, Ann. Oper. Res..

[6]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[7]  Alysson M. Costa.  A survey on benders decomposition applied to fixed-charge network design problems , 2005, Comput. Oper. Res..

[8]  T. C. Hu,et al.  An Application of Generalized Linear Programming to Network Flows , 1962 .

[9]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[10]  Panos M. Pardalos,et al.  Solving Large Scale Fixed Charge Network Flow Problems , 2003 .

[11]  Bruce W. Lamar,et al.  Revised-Modified Penalties for Fixed Charge Transportation Problems , 1997 .

[12]  David K. Smith.  Network Flows: Theory, Algorithms, and Applications , 1994 .

[13]  M. Minoux.  Optimum Synthesis of a Network with Non-Simultaneous Multicommodity Flow Requirements* , 1981 .

[14]  Okitsugu Fujiwara,et al.  Approximate solutions of capacitated fixed-charge minimum cost network flow problems , 1991, Networks.

[15]  Panos M. Pardalos,et al.  A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure , 1999, Oper. Res. Lett..

[16]  Michel Minoux,et al.  Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods , 2001, Ann. Oper. Res..

[17]  W. M. Hirsch,et al.  The fixed charge problem , 1968 .