IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v210y2011i2p185-193.html
   My bibliography  Save this article

A reduction approach to the repeated assignment problem

Author

Listed:
  • Yokoya, Daisuke
  • Duin, Cees W.
  • Yamada, Takeo

Abstract

We consider the repeated assignment problem (RAP), which is a K-fold repetition of the n × n linear assignment problem (LAP), with the additional requirement that no assignment can be repeated more than once. In actual applications K is typically much smaller than n. First, we derive upper and lower bounds respectively by a heuristic together with local search, and an efficient method solving the continuous relaxation. The latter also solves a Lagrangian relaxation, such that the related pegging test, to fix variables at zero or one, decomposes into K independent pegging tests to LAPs. These can be solved exactly by transforming them into all-pairs shortest path problems. Together with these procedures, we also employ a virtual pegging test and reduce RAP in size. Numerical experiments show that the reduced instances, with K

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:185-193
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00729-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    2. Unknown, 1967. "Index," 1967 Conference, August 21-30, 1967, Sydney, New South Wales, Australia 209796, International Association of Agricultural Economists.
    3. 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.
    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. Magos, D. & Miliotis, P., 1994. "An algorithm for the planar three-index assignment problem," European Journal of Operational Research, Elsevier, vol. 77(1), pages 141-153, August.
    6. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    7. Kindervater, G. & Volgenant, A. & de Leve, G. & van Gijlswijk, V., 1985. "On dual solutions of the linear assignment problem," European Journal of Operational Research, Elsevier, vol. 19(1), pages 76-81, January.
    8. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    9. You, Byungjun & Yamada, Takeo, 2007. "A pegging approach to the precedence-constrained knapsack problem," European Journal of Operational Research, Elsevier, vol. 183(2), pages 618-632, 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. 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.
    2. Yanling Chu & Xiaoju Zhang & Zhongzhen Yang, 2017. "Multiple quay cranes scheduling for double cycling in container terminals," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-19, July.
    3. An, Yu & Zhang, Yu & Zeng, Bo, 2015. "The reliable hub-and-spoke design problem: Models and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 103-122.
    4. Dollevoet, Twan & van Essen, J. Theresia & Glorie, Kristiaan M., 2018. "Solution methods for the tray optimization problem," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1070-1084.
    5. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    6. Zhizhu Lai & Qun Yue & Zheng Wang & Dongmei Ge & Yulong Chen & Zhihong Zhou, 2022. "The min-p robust optimization approach for facility location problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1134-1160, September.
    7. Zhang, Zheng & Wei, Yongqi & Xiong, Youming & Peng, Geng & Wang, Guorong & Lu, Jingsheng & Zhong, Lin & Wang, Jingpeng, 2022. "Influence of the location of drilling fluid loss on wellbore temperature distribution during drilling," Energy, Elsevier, vol. 244(PB).
    8. Jabbarzadeh, Armin & Fahimnia, Behnam & Sheu, Jiuh-Biing & Moghadam, Hani Shahmoradi, 2016. "Designing a supply chain resilient to major disruptions and supply/demand interruptions," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 121-149.
    9. Junming Liu & Weiwei Chen & Jingyuan Yang & Hui Xiong & Can Chen, 2022. "Iterative Prediction-and-Optimization for E-Logistics Distribution Network Design," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 769-789, March.
    10. Springborn, Michael R., 2014. "Risk aversion and adaptive management: Insights from a multi-armed bandit model of invasive species risk," Journal of Environmental Economics and Management, Elsevier, vol. 68(2), pages 226-242.
    11. Li, Wenjie & Yang, Lixing & Wang, Li & Zhou, Xuesong & Liu, Ronghui & Gao, Ziyou, 2017. "Eco-reliable path finding in time-variant and stochastic networks," Energy, Elsevier, vol. 121(C), pages 372-387.
    12. Zheng, Jianfeng & Meng, Qiang & Sun, Zhuo, 2014. "Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design," European Journal of Operational Research, Elsevier, vol. 234(3), pages 874-884.
    13. Vasile BRÄ‚TIAN, 2018. "Portfolio Optimization. Application of the Markowitz Model Using Lagrange and Profitability Forecast," Expert Journal of Economics, Sprint Investify, vol. 6(1), pages 26-34.
    14. Miguel A. Lejeune & John Turner, 2019. "Planning Online Advertising Using Gini Indices," Operations Research, INFORMS, vol. 67(5), pages 1222-1245, September.
    15. Claudio Gambella & Joe Naoum-Sawaya & Bissan Ghaddar, 2018. "The Vehicle Routing Problem with Floating Targets: Formulation and Solution Approaches," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 554-569, August.
    16. Xie, Siyang & An, Kun & Ouyang, Yanfeng, 2019. "Planning facility location under generally correlated facility disruptions: Use of supporting stations and quasi-probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 115-139.
    17. Samadi, Mohammadreza & Nikolaev, Alexander & Nagi, Rakesh, 2016. "A subjective evidence model for influence maximization in social networks," Omega, Elsevier, vol. 59(PB), pages 263-278.
    18. Zhang, Zhi-Hai & Jiang, Hai & Pan, Xunzhang, 2012. "A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 140(1), pages 249-255.
    19. Xia, Jun & Wang, Kai & Wang, Shuaian, 2019. "Drone scheduling to monitor vessels in emission control areas," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 174-196.
    20. Gregorio Rius-Sorolla & Julien Maheut & Sofia Estelles-Miguel & Jose P. Garcia-Sabater, 2021. "Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development," Sustainability, MDPI, vol. 13(12), pages 1-23, June.

    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:210:y:2011:i:2:p:185-193. 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.