IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v36y1989i3p283-295.html
   My bibliography  Save this article

Application of generalized benders decomposition to a nonlinear distribution system design problem

Author

Listed:
  • Sangwon Moon

Abstract

The Benders decomposition method has been successfully applied to a classic multistage, multiproduct distribution‐system design problem with fixed and linear variable costs. In other applications, however, distribution‐center variable throughput costs often show nonlinearity due to economies of scale. This article extends the standard problem formulation to a nonlinear distribution‐system design problem and incorporates the generalized Benders decomposition method in an efficient solution algorithm. Approximate dual prices are generated by solving linear instead of concave subproblems. Thereafter these prices are adjusted to induce a more accurate representation of the concave cost function before they are incorporated in the Benders cuts, which are used to generate new binary solutions. The computational results are encouraging.

Suggested Citation

  • Sangwon Moon, 1989. "Application of generalized benders decomposition to a nonlinear distribution system design problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 283-295, June.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:3:p:283-295
    DOI: 10.1002/1520-6750(198906)36:33.0.CO;2-5
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198906)36:33.0.CO;2-5
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198906)36:33.0.CO;2-5?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. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    3. Richard M. Soland, 1974. "Optimal Facility Location with Concave Costs," Operations Research, INFORMS, vol. 22(2), pages 373-382, April.
    4. E. Feldman & F. A. Lehrer & T. L. Ray, 1966. "Warehouse Location Under Continuous Economies of Scale," Management Science, INFORMS, vol. 12(9), pages 670-684, May.
    5. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    6. Alan R. Beckenstein, 1975. "Scale Economies in the Multiplant Firm: Theory and Empirical Evidence," Bell Journal of Economics, The RAND Corporation, vol. 6(2), pages 644-657, Autumn.
    7. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    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. Saif, Ahmed & Elhedhli, Samir, 2016. "Cold supply chain design with environmental considerations: A simulation-optimization approach," European Journal of Operational Research, Elsevier, vol. 251(1), pages 274-287.
    2. 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.
    3. 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.

    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. Kuthambalayan, Thyagaraj S. & Mehta, Peeyush & Shanker, Kripa, 2014. "Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand," European Journal of Operational Research, Elsevier, vol. 237(2), pages 617-627.
    2. Gutierrez, Genaro J. & Kouvelis, Panagiotis & Kurawarwala, Abbas A., 1996. "A robustness approach to uncapacitated network design problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 362-376, October.
    3. Peiling Wu & Joseph C. Hartman & George R. Wilson, 2005. "An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets," Transportation Science, INFORMS, vol. 39(1), pages 87-103, February.
    4. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    5. Brech, Claus-Henning & Ernst, Andreas & Kolisch, Rainer, 2019. "Scheduling medical residents’ training at university hospitals," European Journal of Operational Research, Elsevier, vol. 274(1), pages 253-266.
    6. Halit Üster & Panitan Kewcharoenwong, 2011. "Strategic Design and Analysis of a Relay Network in Truckload Transportation," Transportation Science, INFORMS, vol. 45(4), pages 505-523, November.
    7. Roni, Md.S. & Eksioglu, Sandra D. & Searcy, Erin & Jha, Krishna, 2014. "A supply chain network design model for biomass co-firing in coal-fired power plants," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 115-134.
    8. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    9. Ragheb Rahmaniani & Shabbir Ahmed & Teodor Gabriel Crainic & Michel Gendreau & Walter Rei, 2020. "The Benders Dual Decomposition Method," Operations Research, INFORMS, vol. 68(3), pages 878-895, May.
    10. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    11. Altay, Nezih & Robinson Jr., Powell E. & Bretthauer, Kurt M., 2008. "Exact and heuristic solution approaches for the mixed integer setup knapsack problem," European Journal of Operational Research, Elsevier, vol. 190(3), pages 598-609, November.
    12. 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.
    13. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    14. Jyotirmoy Dalal & Halit Üster, 2018. "Combining Worst Case and Average Case Considerations in an Integrated Emergency Response Network Design Problem," Transportation Science, INFORMS, vol. 52(1), pages 171-188, January.
    15. Halit Üster & Gopalakrishnan Easwaran & Elif Akçali & Sila Çetinkaya, 2007. "Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 890-907, December.
    16. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "Benders Decomposition for Large-Scale Uncapacitated Hub Location," Operations Research, INFORMS, vol. 59(6), pages 1477-1490, December.
    17. Sharma, R.R.K. & Berry, V., 2007. "Developing new formulations and relaxations of single stage capacitated warehouse location problem (SSCWLP): Empirical investigation for assessing relative strengths and computational effort," European Journal of Operational Research, Elsevier, vol. 177(2), pages 803-812, March.
    18. Gopalakrishnan Easwaran & Halit Üster, 2009. "Tabu Search and Benders Decomposition Approaches for a Capacitated Closed-Loop Supply Chain Network Design Problem," Transportation Science, INFORMS, vol. 43(3), pages 301-320, August.
    19. Faria, Victor. A.D. & de Queiroz, Anderson Rodrigo & Lima, Luana M.M. & Lima, José W.M., 2018. "Cooperative game theory and last addition method in the allocation of firm energy rights," Applied Energy, Elsevier, vol. 226(C), pages 905-915.
    20. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.

    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:36:y:1989:i:3:p:283-295. 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.