IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v46y1998i3p368-377.html
   My bibliography  Save this article

A Decomposition Approach for a Class of Economic Equilibrium Models

Author

Listed:
  • Frederic H. Murphy

    (Temple University, Philadelphia, Pennsylvania)

  • Murthy V. Mudrageda

    (Maritrans Management Services, Inc., Philadelphia, Pennsylvania)

Abstract

In this paper we present the theoretical foundations for one of the methods used to achieve convergence in the National Energy Modeling System (NEMS). NEMS is a large model with several component models that are built and operated by different branches in the organization and is an example of a system without a hierarchical structure that cannot be solved by traditional equation solving methods. Some of the component models use linear programs to construct supply and demand curves. The discontinuities that result lead to oscillations in the standard relaxation algorithms. We explain where the convergence problems lie and how the convergence theory with step functions links to the convergence theory with continuous functions. To achieve convergence within the entire system, a set of ad hoc techniques were developed to implement a decomposition strategy that allows the individual models to be run separately. We present the theoretical justification for one of them here. The technique presented here has the potential to allow an organization to use operational models for planning without resorting to aggregation. It also facilitates decentralized computing over Internet.

Suggested Citation

  • Frederic H. Murphy & Murthy V. Mudrageda, 1998. "A Decomposition Approach for a Class of Economic Equilibrium Models," Operations Research, INFORMS, vol. 46(3), pages 368-377, June.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:368-377
    DOI: 10.1287/opre.46.3.368
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.46.3.368
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.46.3.368?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Byong-Hun Ahn & William W. Hogan, 1982. "On Convergence of the PIES Algorithm for Computing Equilibria," Operations Research, INFORMS, vol. 30(2), pages 281-300, April.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. Holmberg, Kaj, 1992. "Linear mean value cross decomposition: A generalization of the Kornai-Liptak method," European Journal of Operational Research, Elsevier, vol. 62(1), pages 55-73, October.
    4. Stella Dafermos & Anna Nagurney, 1984. "Sensitivity Analysis for the General Spatial Economic Equilibrium Problem," Operations Research, INFORMS, vol. 32(5), pages 1069-1086, October.
    5. Frederic H. Murphy & Susan H. Shaw, 1995. "The Evolution of Energy Modeling at the Federal Energy Administration and the Energy Information Administration," Interfaces, INFORMS, vol. 25(5), pages 173-193, October.
    6. Frederic H. Murphy & John J. Conti & Susan H. Shaw & Reginald Sanders, 1988. "Modeling and Forecasting Energy Markets with the Intermediate Future Forecasting System," Operations Research, INFORMS, vol. 36(3), pages 406-420, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Murthy V. Mudrageda & Frederic H. Murphy & Steve Welch, 2004. "Developing Strategies for Maritrans’ Business Units," Interfaces, INFORMS, vol. 34(2), pages 149-161, April.
    2. Fuller, J. David & Chung, William, 2008. "Benders decomposition for a class of variational inequalities," European Journal of Operational Research, Elsevier, vol. 185(1), pages 76-91, February.
    3. William Chung, 2024. "Truncated Dantzig–Wolfe Decomposition for a Class of Constrained Variational Inequality Problems," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 81-104, July.
    4. William Chung & J. D. Fuller & Y. June Wu, 2006. "A New Decomposition Method for Multiregional Economic Equilibrium Models," Operations Research, INFORMS, vol. 54(4), pages 643-655, August.
    5. J. Fuller & William Chung, 2005. "Dantzig—Wolfe Decomposition of Variational Inequalities," Computational Economics, Springer;Society for Computational Economics, vol. 25(4), pages 303-326, June.
    6. Christensen, Adam & Hobbs, Benjamin, 2016. "A model of state and federal biofuel policy: Feasibility assessment of the California Low Carbon Fuel Standard," Applied Energy, Elsevier, vol. 169(C), pages 799-812.
    7. W. Chung & J. Fuller & Y. Wu, 2003. "A New Demand-Supply Decomposition Method for a Class of Economic Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 231-243, June.
    8. René Caldentey & Susana Mondschein, 2003. "Policy Model for Pollution Control in the Copper Industry, Including a Model for the Sulfuric Acid Market," Operations Research, INFORMS, vol. 51(1), pages 1-16, February.
    9. Steven A. Gabriel & Andy S. Kydes & Peter Whitman, 2001. "The National Energy Modeling System: A Large-Scale Energy-Economic Equilibrium Model," Operations Research, INFORMS, vol. 49(1), pages 14-25, February.
    10. William Chung & J. David Fuller, 2010. "Subproblem Approximation in Dantzig-Wolfe Decomposition of Variational Inequality Models with an Application to a Multicommodity Economic Equilibrium Model," Operations Research, INFORMS, vol. 58(5), pages 1318-1327, October.
    11. Frederic Murphy & Axel Pierru & Yves Smeers, 2016. "A Tutorial on Building Policy Models as Mixed-Complementarity Problems," Interfaces, INFORMS, vol. 46(6), pages 465-481, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. W. Chung & J. Fuller & Y. Wu, 2003. "A New Demand-Supply Decomposition Method for a Class of Economic Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 231-243, June.
    2. 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.
    3. 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.
    4. William W. Hogan, 2002. "Energy Modeling for Policy Studies," Operations Research, INFORMS, vol. 50(1), pages 89-95, February.
    5. GABRIEL, Steven & SMEERS, Yves, 2005. "Complementarity problems in restructured natural gas markets," LIDAM Discussion Papers CORE 2005037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. J. Fuller & William Chung, 2005. "Dantzig—Wolfe Decomposition of Variational Inequalities," Computational Economics, Springer;Society for Computational Economics, vol. 25(4), pages 303-326, June.
    7. Yang, Chin W. & Hwang, Ming J. & Sohng, Soong N., 2002. "The Cournot competition in the spatial equilibrium model," Energy Economics, Elsevier, vol. 24(2), pages 139-154, March.
    8. William Chung & J. David Fuller, 2010. "Subproblem Approximation in Dantzig-Wolfe Decomposition of Variational Inequality Models with an Application to a Multicommodity Economic Equilibrium Model," Operations Research, INFORMS, vol. 58(5), pages 1318-1327, October.
    9. Steven A. Gabriel & Andy S. Kydes & Peter Whitman, 2001. "The National Energy Modeling System: A Large-Scale Energy-Economic Equilibrium Model," Operations Research, INFORMS, vol. 49(1), pages 14-25, February.
    10. Walter C. Labys & Chin-wei Yang, 1991. "Advances in the Spatial Equilibrium Modeling of Mineral and Energy Issues," International Regional Science Review, , vol. 14(1), pages 61-94, April.
    11. 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.
    12. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.
    13. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    14. Matar, Walid & Murphy, Frederic & Pierru, Axel & Rioux, Bertrand, 2015. "Lowering Saudi Arabia's fuel consumption and energy system costs without increasing end consumer prices," Energy Economics, Elsevier, vol. 49(C), pages 558-569.
    15. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    16. De Jonghe, C. & Hobbs, B. F. & Belmans, R., 2011. "Integrating short-term demand response into long-term investment planning," Cambridge Working Papers in Economics 1132, Faculty of Economics, University of Cambridge.
    17. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.
    18. Talman, A.J.J. & van der Heyden, L., 1981. "Algorithms for the linear complementarity problem which allow an arbitrary starting point," Research Memorandum FEW 99, Tilburg University, School of Economics and Management.
    19. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    20. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," Working Papers hal-04141039, HAL.

    More about this item

    Keywords

    Economics; large-scale systems;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:368-377. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.