IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v202y2010i3p654-668.html
   My bibliography  Save this article

Lower bounds for the axial three-index assignment problem

Author

Listed:
  • Kim, Bum-Jin
  • Hightower, William L.
  • Hahn, Peter M.
  • Zhu, Yi-Rong
  • Sun, Lu

Abstract

This paper describes new bounding methods for the axial three-index assignment problem (3AP). For calculating 3AP lower bounds, we use a projection method followed by a Hungarian algorithm, based on a new Lagrangian relaxation. We also use a cost transformation scheme, which iteratively transforms 3AP costs in a series of equivalent 3APs, which provides the possibility of improving the 3AP lower bound. These methods produce efficiently computed relatively tight lower bound.

Suggested Citation

  • Kim, Bum-Jin & Hightower, William L. & Hahn, Peter M. & Zhu, Yi-Rong & Sun, Lu, 2010. "Lower bounds for the axial three-index assignment problem," European Journal of Operational Research, Elsevier, vol. 202(3), pages 654-668, May.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:654-668
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00487-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Renata M. Aiex & Mauricio G. C. Resende & Panos M. Pardalos & Gerardo Toraldo, 2005. "GRASP with Path Relinking for Three-Index Assignment," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 224-247, May.
    2. Hahn, Peter M. & Kim, Bum-Jin & Stutzle, Thomas & Kanthak, Sebastian & Hightower, William L. & Samra, Harvind & Ding, Zhi & Guignard, Monique, 2008. "The quadratic three-dimensional assignment problem: Exact and approximate solution methods," European Journal of Operational Research, Elsevier, vol. 184(2), pages 416-428, January.
    3. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    4. Frieze, A. M., 1983. "Complexity of a 3-dimensional assignment problem," European Journal of Operational Research, Elsevier, vol. 13(2), pages 161-164, June.
    5. Crama, Yves & Spieksma, Frits C. R., 1992. "Approximation algorithms for three-dimensional assignment problems with triangle inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 273-279, August.
    6. Huang, Gaofeng & Lim, Andrew, 2006. "A hybrid genetic algorithm for the Three-Index Assignment Problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 249-257, July.
    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. Yokoya, Daisuke & Duin, Cees W. & Yamada, Takeo, 2011. "A reduction approach to the repeated assignment problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 185-193, April.

    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. Boštjan Gabrovšek & Tina Novak & Janez Povh & Darja Rupnik Poklukar & Janez Žerovnik, 2020. "Multiple Hungarian Method for k -Assignment Problem," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    2. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
    3. Renata M. Aiex & Mauricio G. C. Resende & Panos M. Pardalos & Gerardo Toraldo, 2005. "GRASP with Path Relinking for Three-Index Assignment," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 224-247, May.
    4. Lev G. Afraimovich & Maxim D. Emelin, 2022. "Complexity of Solutions Combination for the Three-Index Axial Assignment Problem," Mathematics, MDPI, vol. 10(7), pages 1-10, March.
    5. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    6. Duc Manh Nguyen & Hoai An Le Thi & Tao Pham Dinh, 2014. "Solving the Multidimensional Assignment Problem by a Cross-Entropy method," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 808-823, May.
    7. P. Senthil Kumar, 2020. "Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment," International Journal of Fuzzy System Applications (IJFSA), IGI Global Scientific Publishing, vol. 9(1), pages 1-34, January.
    8. Huang, Gaofeng & Lim, Andrew, 2006. "A hybrid genetic algorithm for the Three-Index Assignment Problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 249-257, July.
    9. Don A. Grundel & Pavlo A. Krokhmal & Carlos A. S. Oliveira & Panos M. Pardalos, 2007. "On the number of local minima for the multidimensional assignment problem," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 1-18, January.
    10. Urban, Timothy L. & Russell, Robert A., 2003. "Scheduling sports competitions on multiple venues," European Journal of Operational Research, Elsevier, vol. 148(2), pages 302-311, July.
    11. P. Senthil Kumar, 2020. "Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 189-222, February.
    12. Krokhmal, Pavlo A. & Pardalos, Panos M., 2009. "Random assignment problems," European Journal of Operational Research, Elsevier, vol. 194(1), pages 1-17, April.
    13. Kyriakakis, Nikolaos A. & Marinaki, Magdalene & Matsatsinis, Nikolaos & Marinakis, Yannis, 2022. "A cumulative unmanned aerial vehicle routing problem approach for humanitarian coverage path planning," European Journal of Operational Research, Elsevier, vol. 300(3), pages 992-1004.
    14. Yokoya, Daisuke & Duin, Cees W. & Yamada, Takeo, 2011. "A reduction approach to the repeated assignment problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 185-193, April.
    15. Arora, Shalini & Puri, M. C., 1998. "A variant of time minimizing assignment problem," European Journal of Operational Research, Elsevier, vol. 110(2), pages 314-325, October.
    16. B. I. Goldengorin & D. S. Malyshev & P. M. Pardalos & V. A. Zamaraev, 2015. "A tolerance-based heuristic approach for the weighted independent set problem," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 433-450, February.
    17. Papahristodoulou, Christos, 2009. "The optimal layout of football players: A case study for AC Milan," MPRA Paper 20102, University Library of Munich, Germany.
    18. Spieksma, Frits C. R. & Woeginger, Gerhard J., 1996. "Geometric three-dimensional assignment problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 611-618, June.
    19. H-J Bandelt & A Maas & F C R Spieksma, 2004. "Local search heuristics for multi-index assignment problems with decomposable costs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 694-704, July.
    20. Kravtsov, M.K. & Lukshin, E.V., 2008. "Polyhedral combinatorics of multi-index axial transportation problems," European Journal of Operational Research, Elsevier, vol. 189(3), pages 920-938, September.

    More about this item

    Keywords

    ;

    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:eee:ejores:v:202:y:2010:i:3:p:654-668. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.