IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i3p897-916.html
   My bibliography  Save this article

Strong formulations for the pooling problem

Author

Listed:
  • Mohammed Alfaki
  • Dag Haugland

Abstract

The pooling problem is a well-studied global optimization problem with applications in oil refining and petrochemical industry. Despite the strong NP-hardness of the problem, which is proved formally in this paper, most instances from the literature have recently been solved efficiently by use of strong formulations. The main contribution from this paper is a new formulation that proves to be stronger than other formulations based on proportion variables. Moreover, we propose a promising branching strategy for the new formulation and provide computational experiments confirming the strength of the new formulation and the effectiveness of the branching strategy. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Mohammed Alfaki & Dag Haugland, 2013. "Strong formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 897-916, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:897-916
    DOI: 10.1007/s10898-012-9875-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9875-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9875-6?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. Sarker, Ruhul A. & Gunn, Eldon A., 1997. "A simple SLP algorithm for solving a class of nonlinear programs," European Journal of Operational Research, Elsevier, vol. 101(1), pages 140-154, August.
    2. R. E. Griffith & R. A. Stewart, 1961. "A Nonlinear Programming Technique for the Optimization of Continuous Processing Systems," Management Science, INFORMS, vol. 7(4), pages 379-392, July.
    3. Jianzhong Zhang & Nae-Heon Kim & L. Lasdon, 1985. "An Improved Successive Linear Programming Algorithm," Management Science, INFORMS, vol. 31(10), pages 1312-1331, October.
    4. Charles Audet & Jack Brimberg & Pierre Hansen & Sébastien Le Digabel & Nenad Mladenovi'{c}, 2004. "Pooling Problem: Alternate Formulations and Solution Methods," Management Science, INFORMS, vol. 50(6), pages 761-776, June.
    5. F. Palacios-Gomez & L. Lasdon & M. Engquist, 1982. "Nonlinear Optimization by Successive Linear Programming," Management Science, INFORMS, vol. 28(10), pages 1106-1120, October.
    6. Hanif D. Sherali & Warren P. Adams & Patrick J. Driscoll, 1998. "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems," Operations Research, INFORMS, vol. 46(3), pages 396-405, June.
    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. Emmanuel Ogbe & Ali Almansoori & Michael Fowler & Ali Elkamel, 2023. "Optimizing Renewable Injection in Integrated Natural Gas Pipeline Networks Using a Multi-Period Programming Approach," Energies, MDPI, vol. 16(6), pages 1-24, March.
    2. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    3. Mohammed Alfaki & Dag Haugland, 2014. "A cost minimization heuristic for the pooling problem," Annals of Operations Research, Springer, vol. 222(1), pages 73-87, November.
    4. Kazda, Kody & Li, Xiang, 2024. "A linear programming approach to difference-of-convex piecewise linear approximation," European Journal of Operational Research, Elsevier, vol. 312(2), pages 493-511.
    5. Kurt M. Anstreicher & Samuel Burer & Kyungchan Park, 2021. "Convex hull representations for bounded products of variables," Journal of Global Optimization, Springer, vol. 80(4), pages 757-778, August.
    6. Yifu Chen & Christos T. Maravelias, 2022. "Variable Bound Tightening and Valid Constraints for Multiperiod Blending," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2073-2090, July.
    7. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2017. "A polynomially solvable case of the pooling problem," Journal of Global Optimization, Springer, vol. 67(3), pages 621-630, March.
    8. Marandi, Ahmadreza & Dahl, Joachim & de Klerk, Etienne, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Other publications TiSEM 981f1428-4d42-4d3f-9a7a-7, Tilburg University, School of Economics and Management.
    9. Radu Baltean-Lugojan & Ruth Misener, 2018. "Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness," Journal of Global Optimization, Springer, vol. 71(4), pages 655-690, August.
    10. Falk M. Hante & Martin Schmidt, 2019. "Complementarity-based nonlinear programming techniques for optimal mixing in gas networks," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 299-323, September.
    11. Ahmadreza Marandi & Joachim Dahl & Etienne Klerk, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Annals of Operations Research, Springer, vol. 265(1), pages 67-92, June.
    12. Santanu S. Dey & Akshay Gupte, 2015. "Analysis of MILP Techniques for the Pooling Problem," Operations Research, INFORMS, vol. 63(2), pages 412-427, April.
    13. Masaki Kimizuka & Sunyoung Kim & Makoto Yamashita, 2019. "Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods," Journal of Global Optimization, Springer, vol. 75(3), pages 631-654, November.
    14. Dag Haugland & Eligius M. T. Hendrix, 2016. "Pooling Problems with Polynomial-Time Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 591-615, August.
    15. Ríos-Mercado, Roger Z. & Borraz-Sánchez, Conrado, 2015. "Optimization problems in natural gas transportation systems: A state-of-the-art review," Applied Energy, Elsevier, vol. 147(C), pages 536-555.

    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. Mohammed Alfaki & Dag Haugland, 2014. "A cost minimization heuristic for the pooling problem," Annals of Operations Research, Springer, vol. 222(1), pages 73-87, November.
    2. Sarker, Ruhul A. & Gunn, Eldon A., 1997. "A simple SLP algorithm for solving a class of nonlinear programs," European Journal of Operational Research, Elsevier, vol. 101(1), pages 140-154, August.
    3. Michelle L. Blom & Christina N. Burt & Adrian R. Pearce & Peter J. Stuckey, 2014. "A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 658-676, November.
    4. Charles Audet & Jack Brimberg & Pierre Hansen & Sébastien Le Digabel & Nenad Mladenovi'{c}, 2004. "Pooling Problem: Alternate Formulations and Solution Methods," Management Science, INFORMS, vol. 50(6), pages 761-776, June.
    5. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    6. Hong, Sung-Pil & Kim, Taegyoon & Lee, Subin, 2019. "A precision pump schedule optimization for the water supply networks with small buffers," Omega, Elsevier, vol. 82(C), pages 24-37.
    7. Mohammed Alfaki & Dag Haugland, 2013. "A multi-commodity flow formulation for the generalized pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 917-937, July.
    8. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    9. Cheng, Xianliang & Feng, Suzhen & Zheng, Hao & Wang, Jinwen & Liu, Shuangquan, 2022. "A hierarchical model in short-term hydro scheduling with unit commitment and head-dependency," Energy, Elsevier, vol. 251(C).
    10. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    11. Anna Danandeh & Bo Zeng & Brent Caldwell & Brian Buckley, 2016. "A Decision Support System for Fuel Supply Chain Design at Tampa Electric Company," Interfaces, INFORMS, vol. 46(6), pages 503-521, December.
    12. Ali, Agha Iqbal & O'Connor, Debra J., 2010. "The impact of distribution system characteristics on computational tractability," European Journal of Operational Research, Elsevier, vol. 200(2), pages 323-333, January.
    13. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    14. Volker Maag & Martin Berger & Anton Winterfeld & Karl-Heinz Küfer, 2010. "A novel non-linear approach to minimal area rectangular packing," Annals of Operations Research, Springer, vol. 179(1), pages 243-260, September.
    15. Daniel de Wolf & Stéphane Auray & Yves Smeers, 2015. "Using Column Generation To Solve A Coal Blending Problem," Post-Print halshs-02396784, HAL.
    16. Anjos, Miguel F. & Vieira, Manuel V.C., 2017. "Mathematical optimization approaches for facility layout problems: The state-of-the-art and future research directions," European Journal of Operational Research, Elsevier, vol. 261(1), pages 1-16.
    17. Chang, Ching-Ter, 2000. "An efficient linearization approach for mixed-integer problems," European Journal of Operational Research, Elsevier, vol. 123(3), pages 652-659, June.
    18. Hanif D. Sherali & Barbara M. P. Fraticelli & Russell D. Meller, 2003. "Enhanced Model Formulations for Optimal Facility Layout," Operations Research, INFORMS, vol. 51(4), pages 629-644, August.
    19. Dudek, Gregor & Stadtler, Hartmut, 2005. "Negotiation-based collaborative planning between supply chains partners," European Journal of Operational Research, Elsevier, vol. 163(3), pages 668-687, June.
    20. Pratik Worah, 2015. "Rank bounds for a hierarchy of Lovász and Schrijver," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 689-709, October.

    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:spr:jglopt:v:56:y:2013:i:3:p:897-916. 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.springer.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.