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A polynomially solvable case of the pooling problem

Author

Listed:
  • Natashia Boland

    (Georgia Institute of Technology)

  • Thomas Kalinowski

    (The University of Newcastle)

  • Fabian Rigterink

    (The University of Newcastle)

Abstract

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the pooling problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0432-6
    DOI: 10.1007/s10898-016-0432-6
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    References listed on IDEAS

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    1. 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.
    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, 2013. "Strong formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 897-916, July.
    4. Santanu S. Dey & Akshay Gupte, 2015. "Analysis of MILP Techniques for the Pooling Problem," Operations Research, INFORMS, vol. 63(2), pages 412-427, April.
    5. Calvin W. DeWitt & Leon S. Lasdon & Allan D. Waren & Donald A. Brenner & Simon A. Melhem, 1989. "OMEGA: An Improved Gasoline Blending System for Texaco," Interfaces, INFORMS, vol. 19(1), pages 85-101, February.
    6. 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.
    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. Billy Rigby & Leon S. Lasdon & Allan D. Waren, 1995. "The Evolution of Texaco’s Blending Systems: From OMEGA to StarBlend," Interfaces, INFORMS, vol. 25(5), pages 64-83, October.
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    Cited by:

    1. 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.
    2. 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.

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