IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v143y2006i1p265-27510.1007-s10479-006-7387-9.html
   My bibliography  Save this article

Max-min sum minimization transportation problem

Author

Listed:
  • Sonia Puri
  • M. Puri

Abstract

A non-convex optimization problem involving minimization of the sum of max and min concave functions over a transportation polytope is studied in this paper. Based upon solving at most (g+1)(> p) cost minimizing transportation problems with m sources and n destinations, a polynomial time algorithm is proposed which minimizes the concave objective function where, p is the number of pairwise disjoint entries in the m× n time matrix {t ij } sorted decreasingly and T g is the minimum value of the max concave function. An exact global minimizer is obtained in a finite number of iterations. A numerical illustration and computational experience on the proposed algorithm is also included. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Sonia Puri & M. Puri, 2006. "Max-min sum minimization transportation problem," Annals of Operations Research, Springer, vol. 143(1), pages 265-275, March.
    • Handle: RePEc:spr:annopr:v:143:y:2006:i:1:p:265-275:10.1007/s10479-006-7387-9
    DOI: 10.1007/s10479-006-7387-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-7387-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-7387-9?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. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    2. Sherali, Hanif D., 1982. "Equivalent weights for lexicographic multi-objective programs: Characterizations and computations," European Journal of Operational Research, Elsevier, vol. 11(4), pages 367-379, December.
    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. Ting Pong & Hao Sun & Ningchuan Wang & Henry Wolkowicz, 2016. "Eigenvalue, quadratic programming, and semidefinite programming relaxations for a cut minimization problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 333-364, March.
    2. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    3. Amitai Armon & Iftah Gamzu & Danny Segev, 2014. "Mobile facility location: combinatorial filtering via weighted occupancy," Journal of Combinatorial Optimization, Springer, vol. 28(2), pages 358-375, August.
    4. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    5. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    6. Amitabh Basu & Jesús A. De Loera & Mark Junod, 2014. "On Chubanov's Method for Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 336-350, May.
    7. Lamghari, Amina & Ferland, Jacques A., 2011. "Assigning judges to competitions of several rounds using Tabu search," European Journal of Operational Research, Elsevier, vol. 210(3), pages 694-705, May.
    8. László A. Végh, 2017. "A Strongly Polynomial Algorithm for Generalized Flow Maximization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 179-211, January.
    9. Mao-Cheng Cai & Xiaoguang Yang & Yanjun Li, 1999. "Inverse Polymatroidal Flow Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 115-126, July.
    10. Fanrong Xie & Anuj Sharma & Zuoan Li, 2022. "An alternate approach to solve two-level priority based assignment problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 613-656, March.
    11. Ilan Adler & Martin Bullinger & Vijay V. Vazirani, 2024. "A Generalization of von Neumann's Reduction from the Assignment Problem to Zero-Sum Games," Papers 2410.10767, arXiv.org.
    12. D. V. Gribanov & D. S. Malyshev & P. M. Pardalos & S. I. Veselov, 2018. "FPT-algorithms for some problems related to integer programming," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1128-1146, May.
    13. Sherali, Hanif D. & Narayanan, Arvind & Sivanandan, R., 2003. "Estimation of origin-destination trip-tables based on a partial set of traffic link volumes," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 815-836, November.
    14. Laura Laguna-Salvadó & Matthieu Lauras & Uche Okongwu & Tina Comes, 2019. "A multicriteria Master Planning DSS for a sustainable humanitarian supply chain," Annals of Operations Research, Springer, vol. 283(1), pages 1303-1343, December.
    15. M. Cai & X. Yang & Y. Li, 2000. "Inverse Problems of Submodular Functions on Digraphs," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 559-575, March.
    16. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    17. Prabhjot Kaur & Anuj Sharma & Vanita Verma & Kalpana Dahiya, 2022. "An alternate approach to solve two-level hierarchical time minimization transportation problem," 4OR, Springer, vol. 20(1), pages 23-61, March.
    18. Paulo Oliveira, 2014. "A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 267-284, December.
    19. Steffen Borgwardt & Stephan Patterson, 2021. "On the computational complexity of finding a sparse Wasserstein barycenter," Journal of Combinatorial Optimization, Springer, vol. 41(3), pages 736-761, April.
    20. Orlin, James B., 1953-., 1988. "A faster strongly polynomial minimum cost flow algorithm," Working papers 2042-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.

    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:annopr:v:143:y:2006:i:1:p:265-275:10.1007/s10479-006-7387-9. 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.