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Letter to the Editor—The Multidimensional Assignment Problem

Author

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  • William P. Pierskalla

    (Case Western Reserve University, Cleveland, Ohio)

Abstract

The multidimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be thought of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch-and-bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem.

Suggested Citation

  • William P. Pierskalla, 1968. "Letter to the Editor—The Multidimensional Assignment Problem," Operations Research, INFORMS, vol. 16(2), pages 422-431, April.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:2:p:422-431
    DOI: 10.1287/opre.16.2.422
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    Citations

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    Cited by:

    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. 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, vol. 9(1), pages 1-34, January.
    3. Benjamin Lev, 2010. "Book Reviews," Interfaces, INFORMS, vol. 40(6), pages 480-485, December.
    4. 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.
    5. 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.
    6. L Wan & J F Bard, 2007. "Weekly staff scheduling with workstation group restrictions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1030-1046, August.
    7. 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.
    8. Alla R. Kammerdiner & Andre N. Guererro, 2019. "Data-driven combinatorial optimization for sensor-based assessment of near falls," Annals of Operations Research, Springer, vol. 276(1), pages 137-153, May.
    9. Mencaroni, Andrea & Claeys, Dieter & Raa, Birger & De Vuyst, Stijn, 2024. "A quantitative framework to support the decision between traditional, selective, and hybrid assembly," International Journal of Production Economics, Elsevier, vol. 273(C).
    10. D. A. Grundel & C. A. S. Oliveira & P. M. Pardalos, 2004. "Asymptotic Properties of Random Multidimensional Assignment Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 487-500, September.
    11. Alla Kammerdiner & Alexander Semenov & Eduardo L. Pasiliao, 2022. "Multidimensional Assignment Problem for Multipartite Entity Resolution," Journal of Global Optimization, Springer, vol. 84(2), pages 491-523, October.
    12. Zvi Drezner & Pawel Kalczynski, 2017. "The continuous grey pattern problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 469-483, May.
    13. Vladyslav Sokol & Ante Ćustić & Abraham P. Punnen & Binay Bhattacharya, 2020. "Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 730-746, July.
    14. Maurice Queyranne & Frits Spieksma & Fabio Tardella, 1998. "A General Class of Greedily Solvable Linear Programs," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 892-908, November.
    15. 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.

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