IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v55y2004i12d10.1057_palgrave.jors.2601806.html
   My bibliography  Save this article

The elastic generalized assignment problem

Author

Listed:
  • R M Nauss

    (University of Missouri–St. Louis,)

Abstract

The generalized assignment problem (GAP) has been studied by numerous researchers over the past 30 years or so. Simply stated, one must find a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honoured. The problem is known to be NP-hard. In this paper, we study the elastic generalized assignment problem (EGAP). The elastic version of GAP allows agent resource capacity to be violated at additional cost. Another version allows undertime costs to be assessed as well if an agent's resource capacity is not used to its full extent. The EGAP is also NP-hard. We describe a special-purpose branch-and-bound algorithm that utilizes linear programming cuts, feasible solution generators, Lagrangean relaxation and subgradient optimization. We present computational results on a large collection of randomly generated ‘hard’ problems with up to 4000 binary variables.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:12:d:10.1057_palgrave.jors.2601806
    DOI: 10.1057/palgrave.jors.2601806
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601806
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2601806?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Laguna, Manuel & Kelly, James P. & Gonzalez-Velarde, JoseLuis & Glover, Fred, 1995. "Tabu search for the multilevel generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 176-189, April.
    2. Cattrysse, Dirk & Degraeve, Zeger & Tistaert, Jurgen, 1998. "Solving the generalised assignment problem using polyhedral results," European Journal of Operational Research, Elsevier, vol. 108(3), pages 618-628, August.
    3. A. M. Geoffrion & R. E. Marsten, 1972. "Integer Programming Algorithms: A Framework and State-of-the-Art Survey," Management Science, INFORMS, vol. 18(9), pages 465-491, May.
    4. 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.
    5. Robert M. Nauss, 1976. "An Efficient Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 23(1), pages 27-31, September.
    6. Monique Guignard & Moshe B. Rosenwein, 1989. "Technical Note—An Improved Dual Based Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 37(4), pages 658-663, August.
    7. Cattrysse, Dirk G. & Van Wassenhove, Luk N., 1992. "A survey of algorithms for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 60(3), pages 260-272, August.
    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. 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, 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.
    4. 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.

    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. 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.
    2. Pessoa, Artur Alves & Hahn, Peter M. & Guignard, Monique & Zhu, Yi-Rong, 2010. "Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique," European Journal of Operational Research, Elsevier, vol. 206(1), pages 54-63, October.
    3. Amini, Mohammad M. & Racer, Michael & Ghandforoush, Parviz, 1998. "Heuristic sensitivity analysis in a combinatoric environment: An exposition and case study," European Journal of Operational Research, Elsevier, vol. 108(3), pages 604-617, August.
    4. June S. Park & Byung Ha Lim & Youngho Lee, 1998. "A Lagrangian Dual-Based Branch-and-Bound Algorithm for the Generalized Multi-Assignment Problem," Management Science, INFORMS, vol. 44(12-Part-2), pages 271-282, December.
    5. Diaz, Juan A. & Fernandez, Elena, 2001. "A Tabu search heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 132(1), pages 22-38, July.
    6. 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.
    7. Klose, Andreas & Drexl, Andreas, 2001. "Combinatorial optimisation problems of the assignment type and a partitioning approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 545, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. 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.
    9. Helena Ramalhinho-Lourenço & Daniel Serra, 1998. "Adaptive approach heuristics for the generalized assignment problem," Economics Working Papers 288, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Lorena, Luiz Antonio N. & Narciso, Marcelo G., 1996. "Relaxation heuristics for a generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 91(3), pages 600-610, June.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Haddadi, Salim & Ouzia, Hacene, 2004. "Effective algorithm and heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 153(1), pages 184-190, February.
    16. 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.
    17. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.
    18. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    19. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    20. Alberto Ceselli & Giovanni Righini, 2006. "A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem," Operations Research, INFORMS, vol. 54(6), pages 1172-1184, December.

    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:pal:jorsoc:v:55:y:2004:i:12:d:10.1057_palgrave.jors.2601806. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    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.