Advertisement

An algorithm for optimizing network flow capacity under economies of scale

  • P. P. Bansai
  • S. E. Jacobsen
Contributed Papers

Abstract

The problem of optimally allocating a fixed budget to the various arcs of a single-source, single-sink network for the purpose of maximizing network flow capacity is considered. The initial vector of arc capacities is given, and the cost function, associated with each arc, for incrementing capacity is concave; therefore, the feasible region is nonconvex. The problem is approached by Benders' decomposition procedure, and a finite algorithm is developed for solving the nonconvex relaxed master problems. A numerical example of optimizing network flow capacity, under economies of scale, is included.

Key Words

Nonconvex programming network flows mathematical programming network synthesis operations research 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fulkerson, D. R.,Increasing the Capacity of a Network, Management Science, Vol. 5, pp. 472–483, 1959.Google Scholar
  2. 2.
    Beale, E. M. L., andTomlin, J. A.,Special Facilities in a Generalized Mathematical Programming System for Nonconvex Problems Using Ordered Sets of Variables, 5th International Conference on Operations Research, Edited by J. Lawrence, Tavistock Publications, London, England, 1969.Google Scholar
  3. 3.
    Tomlin, J. A.,Branch and Bound Methods for Integer and Non-Convex Programming, Integer and Nonlinear Programming, Edited by J. Abadie, North-Holland Publishing Company, Amsterdam, Holland, 1970.Google Scholar
  4. 4.
    Price, W. L.,Increasing the Capacity of a Network Where the Costs Are Non-Linear: A Branch-and-Bound Algorithm, CORS Journal, Vol. 5, pp. 110–114, 1967.Google Scholar
  5. 5.
    Yaged, B., Jr.,Minimum Cost Routing for Static Network Models, Networks, Vol. 1, pp. 139–172, 1971.Google Scholar
  6. 6.
    Soland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, II, Nonconvex Constraints, Management Science, Vol. 17, pp. 759–773, 1971.Google Scholar
  7. 7.
    Rosen, J. B.,Iterative Solution of Nonlinear Optimal Control Problems, SIAM Journal on Control, Vol. 4, pp. 223–244, 1966.Google Scholar
  8. 8.
    Meyer, R.,The Validity of a Family of Optimization Methods, SIAM Journal on Control, Vol. 8, pp. 41–54, 1970.Google Scholar
  9. 9.
    Benders, J. F.,Partitioning Procedures for Solving Mixed-Variables Programming Problems, Numeriche Mathematik, Vol. 4, pp. 238–252, 1962.Google Scholar
  10. 10.
    Geoffrion, A. M.,Generalized Benders Decomposition, Journal of Optimization Theory and Applications, Vol. 4, pp. 237–260, 1972.Google Scholar
  11. 11.
    Bansal, P. P., andJacobsen, S. E.,Characterization of Local Solutions for a Class of Nonconvex Programs, Journal of Optimization Theory and Applications, Vol. 15, No. 5, 1975.Google Scholar
  12. 12.
    Falk, J. E., andSoland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, Management Science, Vol. 15, pp. 550–569, 1969.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • P. P. Bansai
    • 1
  • S. E. Jacobsen
    • 1
  1. 1.Engineering Systems Department, School of Engineering and Applied ScienceUniversity of CaliforniaLos Angeles

Personalised recommendations