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Pooling Problem: Alternate Formulations and Solution Methods

Author

Listed:
  • Charles Audet

    (GERAD and École Polytechnique de Montréal, C.P. 6079, Succursalle Centre-ville, Montréal, Québec, Canada H3C 3A7)

  • Jack Brimberg

    (School of Business Administration, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3)

  • Pierre Hansen

    (GERAD and École des Hautes Études Commerciales, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada H3T 2A7)

  • Sébastien Le Digabel

    (GERAD and École des Hautes Études Commerciales, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada H3T 2A7)

  • Nenad Mladenovi'{c}

    (GERAD and École des Hautes Études Commerciales, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada H3T 2A7)

Abstract

The pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:6:p:761-776
    DOI: 10.1287/mnsc.1030.0207
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    References listed on IDEAS

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    1. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    2. Thomas E. Baker & Leon S. Lasdon, 1985. "Successive Linear Programming at Exxon," Management Science, INFORMS, vol. 31(3), pages 264-274, March.
    3. M. Dür & R. Horst, 1997. "Lagrange Duality and Partitioning Techniques in Nonconvex Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 347-369, November.
    4. 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.
    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. Weldon A. Lodwick, 1992. "Preprocessing Nonlinear Functional Constraints with Applications to the Pooling Problem," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 119-131, May.
    7. 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.
    8. Jianzhong Zhang & Nae-Heon Kim & L. Lasdon, 1985. "An Improved Successive Linear Programming Algorithm," Management Science, INFORMS, vol. 31(10), pages 1312-1331, October.
    9. 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.
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