IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v67y2017i3d10.1007_s10898-016-0434-4.html
   My bibliography  Save this article

Relaxations and discretizations for the pooling problem

Author

Listed:
  • Akshay Gupte

    (Clemson University)

  • Shabbir Ahmed

    (Georgia Institute of Technology)

  • Santanu S. Dey

    (Georgia Institute of Technology)

  • Myun Seok Cheon

    (ExxonMobil Research and Engineering Company)

Abstract

The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques. We also present new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs. Finally, we propose discretization methods for inner approximating the feasible region and obtaining good primal bounds. Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs. The strength of our relaxations and usefulness of our discretizations is empirically validated on random test instances. We report best known primal bounds on some of the large-scale instances.

Suggested Citation

  • Akshay Gupte & Shabbir Ahmed & Santanu S. Dey & Myun Seok Cheon, 2017. "Relaxations and discretizations for the pooling problem," Journal of Global Optimization, Springer, vol. 67(3), pages 631-669, March.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0434-4
    DOI: 10.1007/s10898-016-0434-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0434-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-016-0434-4?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. Xiang Li & Asgeir Tomasgard & Paul Barton, 2012. "Decomposition strategy for the stochastic pooling problem," Journal of Global Optimization, Springer, vol. 54(4), pages 765-790, December.
    2. Josef Kallrath, 2005. "Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 339-373, November.
    3. Manuel Ruiz & Olivier Briant & Jean-Maurice Clochard & Bernard Penz, 2013. "Large-scale standard pooling problems with constrained pools and fixed demands," Journal of Global Optimization, Springer, vol. 56(3), pages 939-956, July.
    4. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    5. Thomas E. Baker & Leon S. Lasdon, 1985. "Successive Linear Programming at Exxon," Management Science, INFORMS, vol. 31(3), pages 264-274, March.
    6. Santanu S. Dey & Akshay Gupte, 2015. "Analysis of MILP Techniques for the Pooling Problem," Operations Research, INFORMS, vol. 63(2), pages 412-427, April.
    7. Harvey J. Greenberg, 1995. "Analyzing the Pooling Problem," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 205-217, May.
    8. 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.
    9. C. E. Bodington & T. E. Baker, 1990. "A History of Mathematical Programming in the Petroleum Industry," Interfaces, INFORMS, vol. 20(4), pages 117-127, August.
    10. Christodoulos A. Floudas & Avanish Aggarwal, 1990. "A Decomposition Strategy for Global Optimum Search in the Pooling Problem," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 225-235, 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. Yifu Chen & Christos T. Maravelias, 2020. "Preprocessing algorithm and tightening constraints for multiperiod blend scheduling: cost minimization," Journal of Global Optimization, Springer, vol. 77(3), pages 603-625, July.
    2. Fischetti, Matteo & Monaci, Michele, 2020. "A branch-and-cut algorithm for Mixed-Integer Bilinear Programming," European Journal of Operational Research, Elsevier, vol. 282(2), pages 506-514.
    3. Djeumou Fomeni, Franklin, 2018. "A multi-objective optimization approach for the blending problem in the tea industry," International Journal of Production Economics, Elsevier, vol. 205(C), pages 179-192.
    4. 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.
    5. 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.
    6. 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.
    7. Xin Cheng & Xiang Li, 2022. "Discretization and global optimization for mixed integer bilinear programming," Journal of Global Optimization, Springer, vol. 84(4), pages 843-867, December.
    8. 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.
    9. Benhamou, Latifa & Giard, Vincent & Khouloud, Mehdi & Fenies, Pierres & Fontane, Frédéric, 2020. "Reverse Blending: An economically efficient approach to the challenge of fertilizer mass customization," International Journal of Production Economics, Elsevier, vol. 226(C).
    10. 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.
    11. Santanu S. Dey & Burak Kocuk & Asteroide Santana, 2020. "Convexifications of rank-one-based substructures in QCQPs and applications to the pooling problem," Journal of Global Optimization, Springer, vol. 77(2), pages 227-272, June.
    12. Xiao Liu & Simge Küçükyavuz & Nilay Noyan, 2017. "Robust multicriteria risk-averse stochastic programming models," Annals of Operations Research, Springer, vol. 259(1), pages 259-294, December.

    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. 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.
    2. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    3. 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.
    4. 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.
    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. Chen, Ruoran & Deng, Tianhu & Huang, Simin & Qin, Ruwen, 2015. "Optimal crude oil procurement under fluctuating price in an oil refinery," European Journal of Operational Research, Elsevier, vol. 245(2), pages 438-445.
    7. Nats Esquejo & Kevin Miller & Kevin Norwood & Ivan Oliveira & Rob Pratt & Ming Zhao, 2015. "Statistical and Optimization Techniques for Laundry Portfolio Optimization at Procter & Gamble," Interfaces, INFORMS, vol. 45(5), pages 444-461, October.
    8. 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.
    9. Gökalp Erbeyoğlu & Ümit Bilge, 2016. "PSO-based and SA-based metaheuristics for bilinear programming problems: an application to the pooling problem," Journal of Heuristics, Springer, vol. 22(2), pages 147-179, April.
    10. Ted Kutz & Mark Davis & Robert Creek & Nick Kenaston & Craig Stenstrom & Margery Connor, 2014. "Optimizing Chevron’s Refineries," Interfaces, INFORMS, vol. 44(1), pages 39-54, February.
    11. Draman, Murat & Kuban Altinel, I & Bajgoric, Nijaz & Tamer Unal, Ali & Birgoren, Burak, 2002. "A clone-based graphical modeler and mathematical model generator for optimal production planning in process industries," European Journal of Operational Research, Elsevier, vol. 137(3), pages 483-496, March.
    12. Lars Hellemo & Asgeir Tomasgard, 2016. "A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 409-444, July.
    13. 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.
    14. Guajardo, Mario & Kylinger, Martin & Rönnqvist, Mikael, 2013. "Speciality oils supply chain optimization: From a decoupled to an integrated planning approach," European Journal of Operational Research, Elsevier, vol. 229(2), pages 540-551.
    15. Benhamou, Latifa & Giard, Vincent & Khouloud, Mehdi & Fenies, Pierres & Fontane, Frédéric, 2020. "Reverse Blending: An economically efficient approach to the challenge of fertilizer mass customization," International Journal of Production Economics, Elsevier, vol. 226(C).
    16. Vidal, Carlos J. & Goetschalckx, Marc, 2001. "A global supply chain model with transfer pricing and transportation cost allocation," European Journal of Operational Research, Elsevier, vol. 129(1), pages 134-158, February.
    17. 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.
    18. 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.
    19. Santanu S. Dey & Akshay Gupte, 2015. "Analysis of MILP Techniques for the Pooling Problem," Operations Research, INFORMS, vol. 63(2), pages 412-427, April.
    20. Santanu S. Dey & Burak Kocuk & Asteroide Santana, 2020. "Convexifications of rank-one-based substructures in QCQPs and applications to the pooling problem," Journal of Global Optimization, Springer, vol. 77(2), pages 227-272, 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:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0434-4. 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.