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Lower bounds for the axial three-index assignment problem

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  • 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
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    References listed on IDEAS

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    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. Unknown, 1967. "Index," 1967 Conference, August 21-30, 1967, Sydney, New South Wales, Australia 209796, International Association of Agricultural Economists.
    4. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    5. Frieze, A. M., 1983. "Complexity of a 3-dimensional assignment problem," European Journal of Operational Research, Elsevier, vol. 13(2), pages 161-164, June.
    6. 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.
    7. 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.
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    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.

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