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A Mathematical Programming Model for Allocation of Natural Gas

Author

Listed:
  • Richard P. O'Neill

    (Louisiana State University, Baton Rouge, Louisiana)

  • Mark Williard

    (Southern University, Baton Rouge, Louisiana)

  • Bert Wilkins

    (Louisiana State University, Baton Rouge, Louisiana)

  • Ralph Pike

    (Louisiana State University, Baton Rouge, Louisiana)

Abstract

This paper presents a methodology for the allocation of natural gas. The model consists of several objective functions, a set of linear constraints, and a set of nonlinear constraints. The objective functions represent allocation in various categories and can be optimized sequentially. The linear constraints represent the conservation of flow equations for the pipeline network and various accounting relationships. The nonlinear constraints represent the momentum balance necessary for each pipe segment, compressor, or valve. The nonlinear constraints are linearized in a method similar to the method of approximate programming (MAP). A matrix generator is used to create the necessary files for the program execution. We have solved example problems with over 250 linear constraints, 240 nonlinear constraints, and 800 structural columns.

Suggested Citation

  • Richard P. O'Neill & Mark Williard & Bert Wilkins & Ralph Pike, 1979. "A Mathematical Programming Model for Allocation of Natural Gas," Operations Research, INFORMS, vol. 27(5), pages 857-873, October.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:5:p:857-873
    DOI: 10.1287/opre.27.5.857
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    Cited by:

    1. Gabriel, Steven A. & Zhuang, Jifang & Kiet, Supat, 2005. "A large-scale linear complementarity model of the North American natural gas market," Energy Economics, Elsevier, vol. 27(4), pages 639-665, July.
    2. Lise, Wietze & Hobbs, Benjamin F. & van Oostvoorn, Frits, 2008. "Natural gas corridors between the EU and its main suppliers: Simulation results with the dynamic GASTALE model," Energy Policy, Elsevier, vol. 36(6), pages 1890-1906, June.
    3. Pantoš, Miloš, 2011. "Market-based congestion management in electric power systems with increased share of natural gas dependent power plants," Energy, Elsevier, vol. 36(7), pages 4244-4255.
    4. Ozelkan, Ertunga C. & D'Ambrosio, Alfred & Teng, S. Gary, 2008. "Optimizing liquefied natural gas terminal design for effective supply-chain operations," International Journal of Production Economics, Elsevier, vol. 111(2), pages 529-542, February.
    5. Egging, Rudolf G. & Gabriel, Steven A., 2006. "Examining market power in the European natural gas market," Energy Policy, Elsevier, vol. 34(17), pages 2762-2778, November.
    6. Safarian, Sahar & Saboohi, Yadollah & Kateb, Movaffaq, 2013. "Evaluation of energy recovery and potential of hydrogen production in Iranian natural gas transmission network," Energy Policy, Elsevier, vol. 61(C), pages 65-77.
    7. S A Gabriel & R García-Bertrand & P Sahakij & A J Conejo, 2006. "A practical approach to approximate bilinear functions in mathematical programming problems by using Schur's decomposition and SOS type 2 variables," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 995-1004, August.
    8. Conrado Borraz-Sánchez & Russell Bent & Scott Backhaus & Hassan Hijazi & Pascal Van Hentenryck, 2016. "Convex Relaxations for Gas Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 645-656, November.
    9. Lise, Wietze & Hobbs, Benjamin F., 2008. "Future evolution of the liberalised European gas market: Simulation results with a dynamic model," Energy, Elsevier, vol. 33(7), pages 989-1004.
    10. 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.
    11. Daniel de Wolf, 2017. "Mathematical Properties of Formulations of the Gas Transmission Problem," Post-Print halshs-02396747, HAL.
    12. Fu, Xueqian & Guo, Qinglai & Sun, Hongbin & Pan, Zhaoguang & Xiong, Wen & Wang, Li, 2017. "Typical scenario set generation algorithm for an integrated energy system based on the Wasserstein distance metric," Energy, Elsevier, vol. 135(C), pages 153-170.
    13. Aouam, Tarik & Rardin, Ronald & Abrache, Jawad, 2010. "Robust strategies for natural gas procurement," European Journal of Operational Research, Elsevier, vol. 205(1), pages 151-158, August.
    14. Steven A. Gabriel & Supat Kiet & Jifang Zhuang, 2005. "A Mixed Complementarity-Based Equilibrium Model of Natural Gas Markets," Operations Research, INFORMS, vol. 53(5), pages 799-818, October.
    15. Jesco Humpola & Felipe Serrano, 2017. "Sufficient pruning conditions for MINLP in gas network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 239-261, March.
    16. 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.
    17. Boucher, Jacqueline & Smeers, Yves, 1985. "Programmation mathématique et modélisation énergétique," L'Actualité Economique, Société Canadienne de Science Economique, vol. 61(1), pages 24-50, mars.
    18. Jesco Humpola & Armin Fügenschuh & Thorsten Koch, 2016. "Valid inequalities for the topology optimization problem in gas network design," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 597-631, July.
    19. Guldmann, Jean-Michel & Wang, Fahui, 1999. "Optimizing the natural gas supply mix of local distribution utilities," European Journal of Operational Research, Elsevier, vol. 112(3), pages 598-612, February.
    20. Mengying Xue & Tianhu Deng & Zuo‐Jun Max Shen, 2019. "Optimizing natural gas pipeline transmission with nonuniform elevation: A new initialization approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 547-564, October.
    21. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.

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