IDEAS home Printed from https://ideas.repec.org/p/zbw/cauman/632.html
   My bibliography  Save this paper

Reducing the elastic generalized assignment problem to the standard generalized assignment problem

Author

Listed:
  • Büther, Marcel

Abstract

The elastic generalized assignment problem (eGAP) is a natural extension of the generalized assignment problem (GAP) where the capacities are not fixed but can be adjusted which is expressed by continuous variables. These variables might be un-bounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of eGAP to GAP which enables us to employ Standard approaches for the GAP. This results into an heuristic, which can be customized in order to provide solutions having an objective value arbitrarily close to the optimal one.

Suggested Citation

  • Büther, Marcel, 2007. "Reducing the elastic generalized assignment problem to the standard generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 632, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:632
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/147551/1/manuskript_632.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Büther, Marcel & Briskorn, Dirk, 2007. "Reducing the 0-1 knapsack problem with a single continuous variable to the standard 0-1 knapsack problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 629, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Robert M. Nauss, 2003. "Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 249-266, August.
    3. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    4. WOLSEY, Laurence A., 2003. "Strong formulations for mixed integer programs: valid inequalities and extended formulations," LIDAM Reprints CORE 1627, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Kaufman, L. & Plastria, F. & Tubeeckx, S., 1985. "The zero-one knapsack problem with equality constraint," European Journal of Operational Research, Elsevier, vol. 19(3), pages 384-389, March.
    6. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    7. R M Nauss, 2004. "The elastic generalized assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1333-1341, December.
    8. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    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. M Büther, 2010. "Reducing the elastic generalized assignment problem to the standard generalized assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1582-1595, November.
    2. Büther, Marcel, 2008. "Beam search for the elastic generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 634, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Büther, Marcel & Briskorn, Dirk, 2007. "Reducing the 0-1 knapsack problem with a single continuous variable to the standard 0-1 knapsack problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 629, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Marius Posta & Jacques Ferland & Philippe Michelon, 2012. "An exact method with variable fixing for solving the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 629-644, July.
    5. Jeet, V. & Kutanoglu, E., 2007. "Lagrangian relaxation guided problem space search heuristics for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1039-1056, November.
    6. M. Gaudioso & L. Moccia & M. F. Monaco, 2010. "Repulsive Assignment Problem," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 255-273, February.
    7. Salim Haddadi, 2019. "Variable-fixing then subgradient optimization guided very large scale neighborhood search for the generalized assignment problem," 4OR, Springer, vol. 17(3), pages 261-295, September.
    8. Bożena Staruch & Bogdan Staruch, 2021. "Competence-based assignment of tasks to workers in factories with demand-driven manufacturing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 553-565, June.
    9. Mehdi Mrad & Anis Gharbi & Mohamed Haouari & Mohamed Kharbeche, 2016. "An optimization-based heuristic for the machine reassignment problem," Annals of Operations Research, Springer, vol. 242(1), pages 115-132, July.
    10. Woodcock, Andrew J. & Wilson, John M., 2010. "A hybrid tabu search/branch & bound approach to solving the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 566-578, December.
    11. Sujeet Kumar Singh & Deepika Rani, 2019. "A branching algorithm to solve binary problem in uncertain environment: an application in machine allocation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 1007-1023, September.
    12. Gelareh, Shahin & Glover, Fred & Guemri, Oualid & Hanafi, Saïd & Nduwayo, Placide & Todosijević, Raca, 2020. "A comparative study of formulations for a cross-dock door assignment problem," Omega, Elsevier, vol. 91(C).
    13. Drexl, Andreas & Jørnsten, Kurt, 2007. "Pricing the generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 627, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    14. Pasquale Avella & Maurizio Boccia & Igor Vasilyev, 2010. "A computational study of exact knapsack separation for the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 45(3), pages 543-555, April.
    15. Ahmed Ghoniem & Tulay Flamand & Mohamed Haouari, 2016. "Optimization-Based Very Large-Scale Neighborhood Search for Generalized Assignment Problems with Location/Allocation Considerations," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 575-588, August.
    16. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    17. Franck Butelle & Laurent Alfandari & Camille Coti & Lucian Finta & Lucas Létocart & Gérard Plateau & Frédéric Roupin & Antoine Rozenknop & Roberto Wolfler Calvo, 2016. "Fast machine reassignment," Annals of Operations Research, Springer, vol. 242(1), pages 133-160, July.
    18. Li, Jing-Quan & Borenstein, Denis & Mirchandani, Pitu B., 2008. "Truck scheduling for solid waste collection in the City of Porto Alegre, Brazil," Omega, Elsevier, vol. 36(6), pages 1133-1149, December.
    19. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    20. Pritibhushan Sinha, 2009. "Assignment problems with changeover cost," Annals of Operations Research, Springer, vol. 172(1), pages 447-457, November.

    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:zbw:cauman:632. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/ibkiede.html .

    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.