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An Overview of Models and Solution Methods for Pooling Problems

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Energy, Natural Resources and Environmental Economics

Part of the book series: Energy Systems ((ENERGY))

Abstract

Network flow models, where the flow quality is given at the supply nodes and quality constraints are defined at the demand nodes, appear frequently when optimizing refinery operations, pipeline gas transportation, and other energy related operations. Tracing the quality of the flow from the supplier to the market implies that the quality must be updated at the nodes where different flow streams are mixed. This results in the well-known pooling problem, the non-linear nature of which makes it hard to solve. In this chapter, I give an overview of available methodology for solving the pooling problem. I distinguish between fast but possibly inexact methods aimed for medium and large scale instances, and more time-consuming exact methods that tackle small instances.

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References

  • Adhya, N., Tawarmalani, M., & Sahinidis, N. V. (1999). A Lagrangian approach to the pooling problem. Industrial and Engineering Chemistry Research, 38(5), 1956–1972

    Article  Google Scholar 

  • Al-Khayyal, F. A., & Falk, J. E. (1983). Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2), 273–286

    Article  Google Scholar 

  • Amos, F., Rönnqvist, M., & Gill, G. (1997). Modelling the pooling problem at the New Zealand Refining Company. Journal of the Operational Research Society, 48(8), 767–778

    Google Scholar 

  • Audet, C., Brimberg, J., Hansen, P., Le Digabel, S., & Mladenović, N. (2004). Pooling problem: Alternate formulations and solution methods. Management Science, 50(6), 761–776

    Article  Google Scholar 

  • Audet, C., Hansen, P., Jaumard, B., & Savard, G. (2000). A branch-and-cut algorithm for nonconvex quadratically constrained quadratic programming. Mathematical Programming, 87(1), 131–152

    Google Scholar 

  • Baker, T. E., & Lasdon, L. S. (1985). Successive linear programming at Exxon. Management Science, 31(3), 264–274

    Article  Google Scholar 

  • Ben-Tal, A., Eiger, G., & Gershovitz, V. (1994). Global minimization by reducing the duality gap. Mathematical programming, 63(2), 193–212

    Article  Google Scholar 

  • DeWitt, C. W., Lasdon, L. S., Waren, A. D., Brenner, D. A., & Melhem, S. A. (1989). OMEGA: An improved gasoline blending system for Texaco. Interfaces, 19(1), 85–101

    Article  Google Scholar 

  • Foulds, L. R., Haugland, D., & Jörnsten, K. (1992). A bilinear approach to the pooling problem. Optimization, 24, 165–180

    Article  Google Scholar 

  • Griffith, R. E., & Stewart, R. A. (1961). A nonlinear programming technique for the optimization of continuous processing systems. Management Science, 7, 379–392

    Article  Google Scholar 

  • Haverly, C. A. (1978). Studies of the behavior of recursion for the pooling problem. ACM SIGMAP Bulletin, 25, 19–28

    Article  Google Scholar 

  • Haverly, C. A. (1979). Behavior of recursion model – more studies. ACM SIGMAP Bulletin, 26, 22–28

    Article  Google Scholar 

  • Main, R. A. (1993). Large recursion models: Practical aspects of recursion techniques. In T. A. Ciriani & R. C. Leachman (Eds.), Optimization in Industry (pp. 241–249). New York, USA: John Wiley & Sons Ltd

    Google Scholar 

  • McCormick, G. P. (1976). Computability of global solutions to factorable non-convex programs: Part I – convex underestimating problems. Mathematical Programming, 10(1), 147–175

    Article  Google Scholar 

  • Palacios-Gomez, F., Lasdon, L. S., & Engquist, M. (1982). Nonlinear optimization by successive linear programming. Management Science, 28(10), 1106–1120

    Article  Google Scholar 

  • Sahinidis, N. V. (1996). BARON: A general purpose global optimization software package. Journal of Global Optimization, 8(2), 201–205

    Article  Google Scholar 

  • Sahinidis, N. V., & Tawarmalani, M. (2005). Accelerating branch-and-bound through a modeling language construct for relaxation specific constraints. Journal of Global Optimization, 32(2), 259–280

    Article  Google Scholar 

  • Sarker, R. A., & Gunn, E. A. (1997). A simple SLP algorithm for solving a class of nonlinear programs. European Journal of Operational Research, 101(1), 140–154

    Article  Google Scholar 

  • Zhang, J., Kim, N. -H., & Lasdon, L. S. (1985). An improved successive linear programming algorithm. Management Science, 31(10), 1312–1331

    Article  Google Scholar 

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Correspondence to Dag Haugland .

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Haugland, D. (2010). An Overview of Models and Solution Methods for Pooling Problems. In: Bjørndal, E., Bjørndal, M., Pardalos, P., Rönnqvist, M. (eds) Energy, Natural Resources and Environmental Economics. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12067-1_26

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  • DOI: https://doi.org/10.1007/978-3-642-12067-1_26

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