Skip to main content
SpringerLink
Log in

Solving the Two-Stage Capacitated Facility Location Problem by the Lagrangian Heuristic

  • Conference paper
Book cover Computational Logistics (ICCL 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7555))

Included in the following conference series:

Abstract

In the two-stage capacitated facility location problem a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work a Lagrangian relaxation is analyzed and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 72.00
Price excludes VAT (USA)
  • Compact, lightweight 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. Avella, P., Boccia, M.: A cutting plane algorithm for the capacitated facility location problem. Computational Optimization and Applications 43, 39–65 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barahona, F., Chudak, F.: Near-optimal solutions to large-scale facility location problems. Discrete Optimization 2, 35–50 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barros, A., Labbé, M.: A general model for the uncapacitated facility and depot location problem. Location Science 2, 173–191 (1994)

    MATH  Google Scholar 

  4. Bloemhof-Ruwaard, J.M., Salomon, M., Van Wassenhove, L.N.: The capacitated distribution and waste disposal problem. European Journal of Operational Research 88, 490–503 (1996)

    Article  MATH  Google Scholar 

  5. Caserta, M., Quiñonez, E.: A cross entropy-based metaheuristic algorithm for large-scale capacitated facility location problems. Journal of the Operational Research Society 60, 1439–1448 (2009)

    Article  MATH  Google Scholar 

  6. Chardaire, P., Lutton, J.L., Sutter, A.: Upper and lower bounds for the two-level simple plant location problem. Annals of Operations Research 86, 117–140 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cornuejols, G., Sridharan, R., Thizy, J.M.: A comparison of heuristics and relaxations for the capacitated plant location problem. European Journal of Operational Research 50, 280–297 (1980)

    Article  Google Scholar 

  8. Daskin, M., Snyder, L., Berger, R.: Logistics Systems: Design and Optimization. Springer, New York (2003)

    Google Scholar 

  9. Filho, V.J., Galvão, R.D.: A tabu search heuristic for the concentrator location problem. Location Science 6, 189–209 (1998)

    Article  Google Scholar 

  10. Gendron, B., Semet, F.: Formulations and relaxations for a multi-echelon capacitated location-distribution problem. Computers & Operations Research 36, 1335–1355 (2009)

    Article  MATH  Google Scholar 

  11. Guignard, M.: Lagrangian relaxation. TOP 11, 151–228 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Klose, A.: An LP-based heuristic for two-stage capacitated facility location problems. Journal of the Operational Research Society 50, 157–166 (1999)

    MATH  Google Scholar 

  13. Klose, A.: A Lagrangian relax and cut approach for the two-stage capacitated facility location problem. European Journal of Operational Research 126, 408–421 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Klose, A., Drexl, A.: Facility location models for distribution system design. European Journal of Operational Research 162, 4–29 (2004)

    Article  MathSciNet  Google Scholar 

  15. Klose, A., Drexl, A.: Lower bounds for the capacitated facility location problem based on column generation. Management Science 51, 1689–1705 (2005)

    Article  MATH  Google Scholar 

  16. Landete, M., Marín, A.: New facets for the two-stage uncapacitated facility location polytope. Computational Optimization and Applications 44, 487–519 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lasdon, L.S.: Optimization Theory for Large Systems, Boston, Dover (2002)

    Google Scholar 

  18. Litvinchev, I., Ozuna, E.L.: Lagrangian bounds and a heuristic for the two-stage capacitated facility location problem. International Journal of Energy Optimization and Engineering 1, 60–72 (2012)

    Article  Google Scholar 

  19. Liu, Y., Zhu, X.: Capacitated fuzzy two-stage location-allocation problem. International Journal of Innovative Computing, Information and Control 3, 987–999 (2007)

    Google Scholar 

  20. Lu, Z., Bostel, N.: A facility location model for logistics systems including reverse flows: The case of remanufacturing activities. Computers & Operations Research 34, 299–323 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Marín, A., Pelegrín, B.: Applying Lagrangian relaxation to the solution of two-stage location problems. Annals of Operation Research 86, 179–198 (1999)

    Article  MATH  Google Scholar 

  22. Marín, A.: Lower bounds for the two-stage uncapacitated facility location problem. European Journal of Operational Research 179, 1126–1142 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Martin, R.: Large Scale Linear and Integer Optimization: A Unified Approach. Kluwer, Boston (1999)

    Book  MATH  Google Scholar 

  24. Melo, M.T., Nickel, S., Saldanha-da-Gama, F.: Facility location and supply chain management – A review. European Journal of Operational Research 196, 401–412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ramos, M.T., Sáenz, S.: Solving capacitated facility location problems by Fenchel cutting planes. Journal of the Operational Research Society 56, 297–306 (2005)

    Article  MATH  Google Scholar 

  26. Sahin, J., Süral, H.: A review of hierarchical facility location models. Computers & Operations Research 34, 2310–2331 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sridharan, R.: A Lagrangian heuristic for the capacitated plant location problem with side constraints. Journal of the Operational Research Society 42, 579–585 (1991)

    MATH  Google Scholar 

  28. Sun, M.: A tabu search heuristic procedure for the capacitated facility location problem. Journal of Heuristics 17, 1–28 (2011)

    Article  Google Scholar 

  29. Tragantalerngsak, S., Holt, J., Ronnqvist, M.: An exact method for the two-echelon, single-source, capacitated facility location problem. European Journal of Operational Research 123, 473–489 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  30. Uysal, M.: Using heuristic search algorithms for predicting the effort of software projects. Applied and Computational Mathematics 8, 251–262 (2009)

    MATH  Google Scholar 

  31. Wollenweber, J.: A multi-stage facility location problem with staircase and splitting of commodities: model, heuristic approach and application. OR Spectrum 30, 655–673 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wolsey, L.A.: Integer Programming. Wiley, New York (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Complex Systems Department, Computing Centre of Russian Academy of Sciences, Moscow, Russia

    Igor Litvinchev

  2. Faculty of Mechanical and Electrical Engineering, Nuevo Leon State University, Monterrey, Mexico

    Edith Lucero Ozuna Espinosa

Authors
  1. Igor Litvinchev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edith Lucero Ozuna Espinosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 1954 Huashan Road, 200030, Shanghai, PRC, China

    Hao Hu

  2. Institut für Wirtschaftsinformatik, Universität Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany

    Xiaoning Shi , Robert Stahlbock  & Stefan Voß ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Litvinchev, I., Ozuna Espinosa, E.L. (2012). Solving the Two-Stage Capacitated Facility Location Problem by the Lagrangian Heuristic. In: Hu, H., Shi, X., Stahlbock, R., Voß, S. (eds) Computational Logistics. ICCL 2012. Lecture Notes in Computer Science, vol 7555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33587-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33587-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33586-0

  • Online ISBN: 978-3-642-33587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation