Skip to main content

A Dynamic Slope Scaling Procedure for the Fixed-Charge Cost Multi-Commodity Network Flow Problem

  • Chapter
Financial Engineering, E-commerce and Supply Chain

Part of the book series: Applied Optimization ((APOP,volume 70))

Abstract

This chapter deals with multi-commodity network flow problems with fixed-charge arc costs. Such problems arise frequently in practice, for instance in supply chain optimization. We generalize a heuristic that was recently developed for the single commodity variant of our problem, so that it can be applied to the multi-commodity case. We evaluate the performance of the heuristic on a set of randimly generated production, inventory, and transportation problems.

The work of this author was supported by the National Science Foundation under Grant No. DMI-0085682.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahuja, K.R., Magnanti, T.L., Orlin, J.B. Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Upper Saddle River, New Jersey, 1993.

    Google Scholar 

  2. Ahuja, R.K., Magnanti, T.L., Orlin, J.B. Reddy, M.R. Applications of Network Optimization. In Network Models, Handbooks of Operations Research and Management Science, Vol. 7, pp. 1–83, 1995.

    Google Scholar 

  3. Anily, S., Federgruen, A., One warehouse multiple retailer system with vehicle routing costs. Management Science, Vol. 36, No. 1, pp. 92–114, 1990.

    Article  Google Scholar 

  4. Balakrishnan, A., Magnanti, T.L., Shulman, A., Wong, R.T. Models for planning capacity expansion in local access telecommunication networks. Annals of Operations Research, Vol. 33, pp. 239–284, 1991.

    Article  Google Scholar 

  5. Barr, R.S., Glover, F., Klingman, D. A new optimization method for large scale fixed charge transportation problems. Operations Research, Vol. 29, pp. 448–463, 1981.

    Article  Google Scholar 

  6. Beamon, B.M. Supply chain design and analysis: Models and methods. International Journal of Production Economics, Vol. 55, pp. 281–294, 1998.

    Article  Google Scholar 

  7. Bienstock, D., Günlük, O. Capacitated Network Design-Polyhedral Structure and Computation. INFORMS Journal on Computing, Vol. 8 (3), pp. 243–259, 1996.

    Article  Google Scholar 

  8. Burns, L.D., Hall, R.W., Blumenfeld, D.E., Daganzo, C.F. Distribution Strategies that minimize transportation and inventory costs. Operations Research, Vol. 33, No. 3, pp. 469–490, 1985.

    Article  Google Scholar 

  9. Cabot, AN., Erengüç, S.S. Some branch-and-bound procedures for fixed-cost transportation problems. Naval Research Logistics Quarterly, Vol. 31, pp. 145–154, 1984.

    Article  Google Scholar 

  10. Chandra, P., and Fisher, M.L., Coordination of production and distribution planning. European Journal of Operational Research, Vol. 72, pp. 503517, 1994.

    Google Scholar 

  11. Crainic, T. G., Frangioni, A., Gendron, B. Bundle-based relaxation methods for multi-commodity capacitated fixed charge network design. Discrete Applied Mathematics, Vol. 112, pp. 73–99, 2001.

    Article  Google Scholar 

  12. Crainic, T.G., Gendreau, M., Farvolden, J. Simplex-BasedTabu Search for the Multicommodity Capacitated Fixed Charge Network Design Problem. Publication CRT-96–07, Centre de recherche sur le transports. Université de Montréal, 1996.

    Google Scholar 

  13. EWoglu, B., Eksioglu, S.D., Pardalos, P.M. Solving Large-Scale Fixed Charge Network Flow Problems. In Variational Inequalities and Equilibrium Models, P. Daniele, F. Giannesi, A. Mangeri (eds.). Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.

    Google Scholar 

  14. Erengüç, S.S., Simpson N.C., Vakharia, A.J. Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research, Vol. 115, pp. 219–236, 1999.

    Article  Google Scholar 

  15. Erickson, R.E., Monma, C.L., Veinott, Jr.,A.F. Send-and-Split method for Minimum-Concave-Cost Network Flows. Mathematics of Operations Research, Vol. 12, pp. 634–664, 1987.

    Article  Google Scholar 

  16. Freling, R., Romeijn, H.E., Romero Morales, D., Wagelmans, A.P.M. A branch-and-price algorithm for the multi-period single-sourcing problem. Research Report 99–12, Department of Industrial and Systems Engineering, University of Florida, 1999.

    Google Scholar 

  17. Garey M.R., Johnson, D.S., Computers and Intractability: A Guide to the Theory ofNP-Completeness. W.H. Freeman and Company, San Francisco, CA, 1979.

    Google Scholar 

  18. Gavish, B. Augmented Lagrangean Based Algorithms for Centralized Network Design. IEEE Transactions on Communications, Vol. 33 (12), pp. 1247–1257, 1985.

    Article  Google Scholar 

  19. Gavish, B. Topological Design of Telecommunications Networks-Local Access Design Methods. Annals of Operations Research, Vol. 33, pp. 17–71, 1991.

    Article  Google Scholar 

  20. Gendron, B., Crainic, T.G., Bounding Procedures for Multi-commodity Capacitated Fixed Charge Network Design Problems. January 1996.

    Google Scholar 

  21. Gray, P. Exact solution of the fixed-charge transportation problem. Operations Research, Vol. 19, pp. 1529–1538, 1971.

    Article  Google Scholar 

  22. Guisewite, G.M., Pardalos, P.M., Complexity Issues in Nonconvex Network Flow Problems. Complexity in Numerical Optimization, pp. 163–179, 1993.

    Google Scholar 

  23. Hirsch, W.M., Dantzig, G.B. The Fixed Charge Problem. Naval Research Logistics Quarterly, Vol. 15, pp. 413–424, 1968.

    Google Scholar 

  24. Hochbaum, D.S., Segev, A. Analysis of a Flow Problem with Fixed Charges. Networks, Vol. 19, pp. 291–312, 1989.

    Article  Google Scholar 

  25. Holmberg, K., Hellstrand, J. Solving the uncapacitated network design problem by a Lagrangean heuristic and branch-and-bound. Operations Research, Vol. 46, Nr. 2, 1998.

    Google Scholar 

  26. Johnson, D.S., Lenstra, J.K., Rinnooy Kan, A.H.G. The complexity of the network design problem. Networks, Vol. 8, pp. 279–285, 1978.

    Article  Google Scholar 

  27. Kennington, J., Unger, E. A new branch-and-bound algorithm for the fixed charge transportation problem. Management Science, Vol. 22, pp. 11161126, 1976.

    Google Scholar 

  28. Kim, D., Pardalos, P.M. A solution scaling approach for the fixed charge network flow problem using a dynamic scaling procedure. Operations Research Letters, Vol. 24, pp. 195–203, 1999.

    Article  Google Scholar 

  29. Lamar, B.W., Wallace, C.A. Revised-modified penalties for fixed charge transportation problems. Management Science, Vol. 43, pp. 1431–1436, 1997.

    Article  Google Scholar 

  30. Lozovanu, D.D. Properties of Optimal Solutions of a Grid Transportation Problem with Concave Function of the flows on the Arcs. Engineering Cybernetics, Vol. 20, pp. 34–38, 1983.

    Google Scholar 

  31. Magnanti, T.L., Wong, R.T. Network Design and Transportation Planning: Model and Algoithm. Transportaion Science, Vol. 18, pp. 1–55, 1984.

    Article  Google Scholar 

  32. Magnanti, Ti., Wong, R.T. Accelerating Benders Decomposition. Operations Research, Vol. 29, Nr. 3, pp. 464–484, 1980.

    Article  Google Scholar 

  33. Murty, K.G. Solving the Fixed Charge Problem by Ranking the Extreme Points. Operations Research, Vol. 16, pp. 268–279, 1968.

    Article  Google Scholar 

  34. Palekar, U.S., Karwan, M.H., Zionts, S. A branch-and-bound method for fixed charge transportation problem. Management Science, Vol. 36, pp. 1092–1105, 1990.

    Article  Google Scholar 

  35. Romeijn, H.E., Romero Morales, D. An asymptotically optimal greedy heuristic for the multi-period single-sourcing problem: the cyclic case. Research Report 99–11, Department of Industrial and Systems Engineering, University of Florida, 1999.

    Google Scholar 

  36. Romeijn, H.E., Romero Morales, D. Asymptotic analysis of a greedy heuristic for the multi-period single-sourcing problem: the acyclic case. Research Report 99–13, Department of Industrial and Systems Engineering, University of Florida, 1999.

    Google Scholar 

  37. Romeijn, H.E., Romero Morales, D. A greedy heuristic for a three-level multi-period single-sourcing problem. Research Report 2000–3, Department of Industrial and Systems Engineering, University of Florida, 2000.

    Google Scholar 

  38. Romeijn, H.E., Romero Morales, D. A probabilistic analysis of the multi-period single-sourcing problem. Discrete Applied Mathematics, Vol. 112, pp. 301–328, 2001.

    Article  Google Scholar 

  39. Vidal, C.J., Goetschalckx, M. Strategic production-distribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research, Vol. 98, pp. 1–18, 1997.

    Article  Google Scholar 

  40. Wu, S.D., Golbasi, H. Manufacturing Planning over Alternative Facilities: Modeling, Analysis, and Algorithms. In Supply Chain Management: Models, Applications, and Research Directions, J. Geunes, P.M. Pardalos, H.E. Romeijn (eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 279–316, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ekşioğlu, S.D., Pardalos, P.M., Romeijn, H.E. (2002). A Dynamic Slope Scaling Procedure for the Fixed-Charge Cost Multi-Commodity Network Flow Problem. In: Pardalos, P.M., Tsitsiringos, V.K. (eds) Financial Engineering, E-commerce and Supply Chain. Applied Optimization, vol 70. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5226-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-5226-7_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5222-6

  • Online ISBN: 978-1-4757-5226-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics