IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v16y2016i3d10.1007_s12351-015-0205-x.html
   My bibliography  Save this article

Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method

Author

Listed:
  • A. Karakitsiou

    (Technological Educational Institute of Central Macedonia)

  • A. Migdalas

    (Luleå University of Technology)

Abstract

Many problems in supply chain optimization concern the minimization of a differentiable convex objective function subject to a set of linear constraints. The aim of this work is to present a number of such problems and to propose an efficient method for their solution. The proposed method is based on improvements of the well known Frank–Wolfe algorithm. The computational results of the proposed algorithm demonstrate its effectiveness and efficiency.

Suggested Citation

  • A. Karakitsiou & A. Migdalas, 2016. "Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method," Operational Research, Springer, vol. 16(3), pages 401-421, October.
  • Handle: RePEc:spr:operea:v:16:y:2016:i:3:d:10.1007_s12351-015-0205-x
    DOI: 10.1007/s12351-015-0205-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-015-0205-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12351-015-0205-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Holmberg, Kaj & Jornsten, Kurt O., 1984. "Cross decomposition applied to the stochastic transportation problem," European Journal of Operational Research, Elsevier, vol. 17(3), pages 361-368, September.
    2. Arthur M. Geoffrion & Richard F. Powers, 1995. "Twenty Years of Strategic Distribution System Design: An Evolutionary Perspective," Interfaces, INFORMS, vol. 25(5), pages 105-127, October.
    3. Michel L. Balinski, 1961. "Fixed‐cost transportation problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(1), pages 41-54, March.
    4. Guillermo Gallego, 1990. "Scheduling the Production of Several Items with Random Demands in a Single Facility," Management Science, INFORMS, vol. 36(12), pages 1579-1592, December.
    5. Torbjörn Larsson & Michael Patriksson, 1992. "Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 26(1), pages 4-17, February.
    6. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    7. Rachel R. Chen & Robin O. Roundy & Rachel Q. Zhang & Ganesh Janakiraman, 2005. "Efficient Auction Mechanisms for Supply Chain Procurement," Management Science, INFORMS, vol. 51(3), pages 467-482, March.
    8. Leon Cooper & Larry J. Leblanc, 1977. "Stochastic transportation problems and other newtork related convex problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(2), pages 327-337, June.
    9. Larry J. LeBlanc & Richard V. Helgason & David E. Boyce, 1985. "Improved Efficiency of the Frank-Wolfe Algorithm for Convex Network Programs," Transportation Science, INFORMS, vol. 19(4), pages 445-462, November.
    Full references (including those not matched with items on IDEAS)

    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. Maria Daneva & Torbjörn Larsson & Michael Patriksson & Clas Rydergren, 2010. "A comparison of feasible direction methods for the stochastic transportation problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 451-466, July.
    2. Sang Nguyen & Stefano Pallottino & Federico Malucelli, 2001. "A Modeling Framework for Passenger Assignment on a Transport Network with Timetables," Transportation Science, INFORMS, vol. 35(3), pages 238-249, August.
    3. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2020. "Aggregation, disaggregation and decomposition methods in traffic assignment: historical perspectives and new trends," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 199-223.
    4. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    5. Taesung Hwang, 2021. "Assignment of Freight Truck Shipment on the U.S. Highway Network," Sustainability, MDPI, vol. 13(11), pages 1-11, June.
    6. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    7. Jayakrishnan, R. & Tsai, Wei K. & Oh, Jun-Seok & Adler, Jeffrey, 1999. "Event-based ATIS: Practical Implementation and Evaluation of Optimized Strategies (Part I)," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0hz5n8x2, Institute of Transportation Studies, UC Berkeley.
    8. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    9. Takashi Akamatsu, 2001. "An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues," Transportation Science, INFORMS, vol. 35(4), pages 389-404, November.
    10. Damberg, Olof & Lundgren, Jan T. & Patriksson, Michael, 1996. "An algorithm for the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 115-131, April.
    11. Meruza Kubentayeva & Alexander Gasnikov, 2021. "Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    12. David Di Lorenzo & Alessandro Galligari & Marco Sciandrone, 2015. "A convergent and efficient decomposition method for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 60(1), pages 151-170, January.
    13. Yuan, Yun & Yu, Jie, 2018. "Locating transit hubs in a multi-modal transportation network: A cluster-based optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 85-103.
    14. Meng Li & Guowei Hua & Haijun Huang, 2018. "A Multi-Modal Route Choice Model with Ridesharing and Public Transit," Sustainability, MDPI, vol. 10(11), pages 1-14, November.
    15. Guillaume Sagnol & Edouard Pauwels, 2019. "An unexpected connection between Bayes A-optimal designs and the group lasso," Statistical Papers, Springer, vol. 60(2), pages 565-584, April.
    16. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    17. McKelvey, Bill & Wycisk, Christine & Hülsmann, Michael, 2009. "Designing an electronic auction market for complex 'smart parts' logistics: Options based on LeBaron's computational stock market," International Journal of Production Economics, Elsevier, vol. 120(2), pages 476-494, August.
    18. Abdelfettah Laouzai & Rachid Ouafi, 2022. "A prediction model for atmospheric pollution reduction from urban traffic," Environment and Planning B, , vol. 49(2), pages 566-584, February.
    19. Chou, Chang-Chi & Chiang, Wen-Chu & Chen, Albert Y., 2022. "Emergency medical response in mass casualty incidents considering the traffic congestions in proximity on-site and hospital delays," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    20. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.

    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:spr:operea:v:16:y:2016:i:3:d:10.1007_s12351-015-0205-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.