IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v191y2008i2p582-586.html
   My bibliography  Save this article

An asymptotic approximation scheme for the concave cost bin packing problem

Author

Listed:
  • Leung, Joseph Y.-T.
  • Li, Chung-Lun

Abstract

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant [epsilon], there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1Â +Â [epsilon].

Suggested Citation

  • Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "An asymptotic approximation scheme for the concave cost bin packing problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 582-586, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:582-586
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00892-2
    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. Crainic, Teodor Gabriel & Perboli, Guido & Pezzuto, Miriam & Tadei, Roberto, 2007. "Computing the asymptotic worst-case of bin packing lower bounds," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1295-1303, December.
    2. Kang, Jangha & Park, Sungsoo, 2003. "Algorithms for the variable sized bin packing problem," European Journal of Operational Research, Elsevier, vol. 147(2), pages 365-372, June.
    3. Jian Yang & Joseph Y.-T. Leung, 2003. "The Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 51(5), pages 759-770, October.
    4. Alves, Claudio & Valerio de Carvalho, J.M., 2007. "Accelerating column generation for variable sized bin-packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1333-1352, December.
    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. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).
    2. Hu, Qian & Wei, Lijun & Lim, Andrew, 2018. "The two-dimensional vector packing problem with general costs," Omega, Elsevier, vol. 74(C), pages 59-69.
    3. Haouari, Mohamed & Mhiri, Mariem, 2024. "Lower and upper bounding procedures for the bin packing problem with concave loading cost," European Journal of Operational Research, Elsevier, vol. 312(1), pages 56-69.
    4. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
    5. Hu, Qian & Zhu, Wenbin & Qin, Hu & Lim, Andrew, 2017. "A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function," European Journal of Operational Research, Elsevier, vol. 260(1), pages 70-80.
    6. Wang, Ting & Hu, Qian & Lim, Andrew, 2022. "An exact algorithm for two-dimensional vector packing problem with volumetric weight and general costs," European Journal of Operational Research, Elsevier, vol. 300(1), pages 20-34.

    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. Baldi, Mauro Maria & Crainic, Teodor Gabriel & Perboli, Guido & Tadei, Roberto, 2012. "The generalized bin packing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(6), pages 1205-1220.
    2. Mauro Baldi & Teodor Crainic & Guido Perboli & Roberto Tadei, 2014. "Branch-and-price and beam search algorithms for the Variable Cost and Size Bin Packing Problem with optional items," Annals of Operations Research, Springer, vol. 222(1), pages 125-141, November.
    3. Andrea Bettinelli & Alberto Ceselli & Giovanni Righini, 2010. "A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint," Annals of Operations Research, Springer, vol. 179(1), pages 221-241, September.
    4. Qi Zhang & Shixin Liu & Ruiyou Zhang & Shujin Qin, 2021. "Column generation algorithms for mother plate design in steel plants," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 127-153, March.
    5. Lewis, R. & Song, X. & Dowsland, K. & Thompson, J., 2011. "An investigation into two bin packing problems with ordering and orientation implications," European Journal of Operational Research, Elsevier, vol. 213(1), pages 52-65, August.
    6. Qin, Hu & Zhang, Zizhen & Qi, Zhuxuan & Lim, Andrew, 2014. "The freight consolidation and containerization problem," European Journal of Operational Research, Elsevier, vol. 234(1), pages 37-48.
    7. Ekici, Ali, 2023. "A large neighborhood search algorithm and lower bounds for the variable-Sized bin packing problem with conflicts," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1007-1020.
    8. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    9. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2021. "Queue-constrained packing: A vehicle ferry case study," European Journal of Operational Research, Elsevier, vol. 289(2), pages 727-741.
    10. C Alves & J M Valério de Carvalho, 2008. "New integer programming formulations and an exact algorithm for the ordered cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1520-1531, November.
    11. Xueqi Wu & Zhi‐Long Chen, 2022. "Fulfillment scheduling for buy‐online‐pickup‐in‐store orders," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2982-3003, July.
    12. Baldi, Mauro Maria & Manerba, Daniele & Perboli, Guido & Tadei, Roberto, 2019. "A Generalized Bin Packing Problem for parcel delivery in last-mile logistics," European Journal of Operational Research, Elsevier, vol. 274(3), pages 990-999.
    13. Hu, Qian & Wei, Lijun & Lim, Andrew, 2018. "The two-dimensional vector packing problem with general costs," Omega, Elsevier, vol. 74(C), pages 59-69.
    14. Braune, Roland, 2019. "Lower bounds for a bin packing problem with linear usage cost," European Journal of Operational Research, Elsevier, vol. 274(1), pages 49-64.
    15. Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
    16. Witteman, Max & Deng, Qichen & Santos, Bruno F., 2021. "A bin packing approach to solve the aircraft maintenance task allocation problem," European Journal of Operational Research, Elsevier, vol. 294(1), pages 365-376.
    17. van der Gaast, J.P. & Rietveld, C.A. & Gabor, A.F. & Zhang, Y., 2011. "A Local Search Algorithm for Clustering in Software as a Service Networks," ERIM Report Series Research in Management ERS-2011-004-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    18. Goldberg, Noam & Karhi, Shlomo, 2019. "Online packing of arbitrary sized items into designated and multipurpose bins," European Journal of Operational Research, Elsevier, vol. 279(1), pages 54-67.
    19. Liao, Chung-Shou & Hsu, Chia-Hong, 2013. "New lower bounds for the three-dimensional orthogonal bin packing problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 244-252.
    20. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.

    More about this item

    Statistics

    Access and download statistics

    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:191:y:2008:i:2:p:582-586. 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.