IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v39y1992i2p191-212.html
   My bibliography  Save this article

A dual‐based optimization procedure for the two‐echelon uncapacitated facility location problem

Author

Listed:
  • Li‐Lian Gao
  • E. Powell Robinson

Abstract

The two‐echelon uncapacitated facility location problem (TUFLP) is a generalization of the uncapacitated facility location problem (UFLP) and multiactivity facility location problem (MAFLP). In TUFLP there are two echelons of facilities through which products may flow in route to final customers. The objective is to determine the least‐cost number and locations of facilities at each echelon in the system, the flow of product between facilities, and the assignment of customers to supplying facilities. We propose a new dual‐based solution procedure for TUFLP that can be used as a heuristic or incorporated into branch‐and‐bound procedures to obtain optimal solutions to TUFLP. The algorithm is an extension of the dual ascent and adjustment procedures developed by Erlenkotter for UFLP. We report computational experience gained by solving over 420 test problems. The largest problems solved have 25 possible facility locations at each echelon and 35 customer zones, implying 650 integer variables and 21,875 continuous variables.

Suggested Citation

  • Li‐Lian Gao & E. Powell Robinson, 1992. "A dual‐based optimization procedure for the two‐echelon uncapacitated facility location problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 191-212, March.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:2:p:191-212
    DOI: 10.1002/1520-6750(199203)39:23.0.CO;2-T
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199203)39:23.0.CO;2-T
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199203)39:23.0.CO;2-T?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    2. Ro, Hyung-bong & Tcha, Dong-wan, 1984. "A branch and bound algorithm for the two-level uncapacitated facility location problem with some side constraints," European Journal of Operational Research, Elsevier, vol. 18(3), pages 349-358, December.
    3. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    4. Tcha, Dong-wan & Lee, Bum-il, 1984. "A branch-and-bound algorithm for the multi-level uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 18(1), pages 35-43, October.
    5. Basheer M. Khumawala, 1972. "An Efficient Branch and Bound Algorithm for the Warehouse Location Problem," Management Science, INFORMS, vol. 18(12), pages 718-731, August.
    6. M. A. Efroymson & T. L. Ray, 1966. "A Branch-Bound Algorithm for Plant Location," Operations Research, INFORMS, vol. 14(3), pages 361-368, June.
    7. Krarup, Jakob & Pruzan, Peter Mark, 1983. "The simple plant location problem: Survey and synthesis," European Journal of Operational Research, Elsevier, vol. 12(1), pages 36-57, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chandra Ade Irawan & Dylan Jones, 2019. "Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities," Annals of Operations Research, Springer, vol. 272(1), pages 41-67, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    3. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    4. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    5. Holzapfel, Andreas & Potoczki, Tobias & Kuhn, Heinrich, 2023. "Designing the breadth and depth of distribution networks in the retail trade," International Journal of Production Economics, Elsevier, vol. 257(C).
    6. Harkness, Joseph & ReVelle, Charles, 2003. "Facility location with increasing production costs," European Journal of Operational Research, Elsevier, vol. 145(1), pages 1-13, February.
    7. Melachrinoudis, Emanuel & Min, Hokey, 2000. "The dynamic relocation and phase-out of a hybrid, two-echelon plant/warehousing facility: A multiple objective approach," European Journal of Operational Research, Elsevier, vol. 123(1), pages 1-15, May.
    8. Mohammad Ehsanifar & David A. Wood & Arezoo Babaie, 2021. "UTASTAR method and its application in multi-criteria warehouse location selection," Operations Management Research, Springer, vol. 14(1), pages 202-215, June.
    9. Pierre Hansen & Jack Brimberg & Dragan Urošević & Nenad Mladenović, 2007. "Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 552-564, November.
    10. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2017. "Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 767-779, November.
    11. Verter, Vedat & Dasci, Abdullah, 2002. "The plant location and flexible technology acquisition problem," European Journal of Operational Research, Elsevier, vol. 136(2), pages 366-382, January.
    12. H K Smith & G Laporte & P R Harper, 2009. "Locational analysis: highlights of growth to maturity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 140-148, May.
    13. Keskin, Burcu B. & Uster, Halit, 2007. "Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 663-682, October.
    14. Dasci, Abdullah & Verter, Vedat, 2001. "A continuous model for production-distribution system design," European Journal of Operational Research, Elsevier, vol. 129(2), pages 287-298, March.
    15. Mercedes Landete & Alfredo Marín, 2009. "New facets for the two-stage uncapacitated facility location polytope," Computational Optimization and Applications, Springer, vol. 44(3), pages 487-519, December.
    16. Hammami, Ramzi & Frein, Yannick & Hadj-Alouane, Atidel B., 2009. "A strategic-tactical model for the supply chain design in the delocalization context: Mathematical formulation and a case study," International Journal of Production Economics, Elsevier, vol. 122(1), pages 351-365, November.
    17. García Cáceres, Rafael Guillermo & Aráoz Durand, Julián Arturo & Gómez, Fernando Palacios, 2009. "Integral analysis method - IAM," European Journal of Operational Research, Elsevier, vol. 192(3), pages 891-903, February.
    18. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2019. "An Exact Algorithm for Multilevel Uncapacitated Facility Location," Transportation Science, INFORMS, vol. 53(4), pages 1085-1106, July.
    19. Kurt Jörnsten & Andreas Klose, 2016. "An improved Lagrangian relaxation and dual ascent approach to facility location problems," Computational Management Science, Springer, vol. 13(3), pages 317-348, July.
    20. Monabbati, Ehsan & Kakhki, Hossein Taghizadeh, 2015. "On a class of subadditive duals for the uncapacitated facility location problem," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 118-131.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:39:y:1992:i:2:p:191-212. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.