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Solving the Pipe Network Analysis Problem Using Optimization Techniques

Author

Listed:
  • M. Collins

    (Southern Methodist University)

  • L. Cooper

    (Southern Methodist University)

  • R. Helgason

    (Southern Methodist University)

  • J. Kennington

    (Southern Methodist University)

  • L. LeBlanc

    (Southern Methodist University)

Abstract

For more than forty years, approximate solutions for the classical pipe network analysis problem have been obtained by direct solution of the nonlinear stationary point conditions. We propose a revolutionary new approach involving optimization techniques for solving this well-known engineering problem. It is shown that the pipe network analysis problem may be described mathematically in terms of a nonlinear convex cost network flow problem. Three mathematical programming algorithms for solving this problem have been coded and are computationally compared with a code using the traditional Newton-Raphson technique. The computational experience demonstrates that this new approach provides an attractive alternative for solving this important problem.

Suggested Citation

  • M. Collins & L. Cooper & R. Helgason & J. Kennington & L. LeBlanc, 1978. "Solving the Pipe Network Analysis Problem Using Optimization Techniques," Management Science, INFORMS, vol. 24(7), pages 747-760, March.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:7:p:747-760
    DOI: 10.1287/mnsc.24.7.747
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    Citations

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    Cited by:

    1. Antoine Gautier & Frieda Granot, 1996. "Ripples, complements, and substitutes in generalized networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 1-21, February.
    2. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Computing technical capacities in the European entry-exit gas market is NP-hard," Annals of Operations Research, Springer, vol. 295(1), pages 337-362, December.
    3. Lonnie Turpin & Barron Brown, 2021. "On Reworks in a Serial Process with Flexible Windows of Time," SN Operations Research Forum, Springer, vol. 2(2), pages 1-13, June.
    4. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2022. "Global optimization for the multilevel European gas market system with nonlinear flow models on trees," Journal of Global Optimization, Springer, vol. 82(3), pages 627-653, March.
    5. Ralf Lenz & Kai Helge Becker, 2022. "Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 179-224, March.
    6. D’Ambrosio, Claudia & Lodi, Andrea & Wiese, Sven & Bragalli, Cristiana, 2015. "Mathematical programming techniques in water network optimization," European Journal of Operational Research, Elsevier, vol. 243(3), pages 774-788.
    7. Marins, Fernando A. S. & Senne, Edson L. F. & Darby-Dowman, Ken & Machado, Arlene F. & Perin, Clovis, 1997. "Algorithms for network piecewise-linear programs: A comparative study," European Journal of Operational Research, Elsevier, vol. 97(1), pages 183-199, February.
    8. Martin Robinius & Lars Schewe & Martin Schmidt & Detlef Stolten & Johannes Thürauf & Lara Welder, 2019. "Robust optimal discrete arc sizing for tree-shaped potential networks," Computational Optimization and Applications, Springer, vol. 73(3), pages 791-819, July.
    9. Jesco Humpola & Armin Fügenschuh, 2015. "Convex reformulations for solving a nonlinear network design problem," Computational Optimization and Applications, Springer, vol. 62(3), pages 717-759, December.
    10. Brkic, Dejan, 2009. "An improvement of Hardy Cross method applied on looped spatial natural gas distribution networks," Applied Energy, Elsevier, vol. 86(7-8), pages 1290-1300, July.
    11. Spyros Kontogiorgis, 2000. "Practical Piecewise-Linear Approximation for Monotropic Optimization," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 324-340, November.
    12. 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.
    13. J. David Allen & Richard V. Helgason & Jeffery L. Kennington, 1987. "The frequency assignment problem: A solution via nonlinear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 133-139, February.
    14. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.

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