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Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics

Received: 1 March 2021     Accepted: 17 March 2021     Published: 26 March 2021
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Abstract

The TD-BU methodology covers a wide range of objects of various "physical" nature and with various analysis tasks. The feature of such objects is that they have a hierarchical structure. Mathematically, they are related by the formalization of upper-level processes by algebraic equations, while lower levels are described by means of mathematical programming. Currently being extensively researched the forecast status of ultra-large hierarchical systems such as "the country's economy - its fuel and energy complex" with certain requirements. The excessive dimensions of such systems create difficulties in their analysis in the classical formulation, so most researchers use diacoptic methods and therefore these tasks TD-BU are labor-intensive. There are a large number of objects to which the TD-BU methodology could be formally applied. We are talking, among other things, about forecasting the volume of production of all types of products, services and demand for them what is necessary for the activities of all sectors of the economy with details at hierarchical levels. For the tasks of this type the key is the problem of discrepancy of the upper and lower levels indicators. This problem cannot be solved by existing TD-BU models. This paper presents a mathematical model and methods for analytical determination of indicators of the upper and lower levels in the above problems, which solve the problem of ambiguity. The mathematical model is formed in such a way that provides an opportunity to find solutions for the upper and each of the lower (sectoral) levels in a unique, analytical form. Therefore, the search for solutions is non-iterative and not laborious. It is carried out in two stages. On the first of them, using known (standard) methods, forecasts are developed for preliminary indicators of the upper and lower levels. At the second stage a special system of algebraic equations is formed, from which analytical dependences for calculation of refined indicators of both levels are defined. This ensures a complete match between the upper indicator and the sum of the lower levels indicators, which is demonstrated by the example of forecasting electricity demand. These mathematical models and methods can also be used to reconcile the reporting indicators of the upper and lower levels of the respective objects (management structures, banks, trade network, etc.). Thus the coordinated decisions are formed in one stage.

Published in American Journal of Electrical and Computer Engineering (Volume 5, Issue 1)
DOI 10.11648/j.ajece.20210501.14
Page(s) 25-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Top-Down, Bottom-Up, Iteration, Matrix, Discrepancy, Coincidence

References
[1] Jacobsen H. K. (1998) Integrating the bottom-up and top-down approach to energy – economy modelling: the case of Denmark. Energy Economics, 20, 443-461.
[2] Rivers N. & Jaccard M. (2005) Combining Top-Down and Bottom-Up Approaches To Energy-Economy Modeling Using Discrete Choice Methods. The Energy Journal, 26 (1), 83-106.
[3] C. Böhringer C. (1998) “he Synthesis of Bottom-Up and Top-Down in Energy Policy Modeling. Energy Economics, 20 (3), 233–248.
[4] Frei C. W., Hadi P.-A. & Sarlos G. (2003) Dynamic formulation of a top-down and bottom-up merging energy policy model. Energy Policy, 31 (10), 1017–1031.
[5] Böhringer C. & Rutherford T. F. (2008) Combining bottom-up and top-down. Energy Economics, 30 (2), 574-596.
[6] Helgesen P. J. (2013) Top-down and Bottom-up: Combining energy system models and macroeconomic general equilibrium models. CenSES working paper 1/2013, [online]. Available: http://www.ntnu.no/censes/working-papers.
[7] Murphy R. N., Rivers N. & Jaccard M. (2007) Hybrid modeling of industrial energy consumption and greenhouse gas emissions with an application to Canada. Energy Economics, 29 (4), 826-846
[8] Strachan N. & Kannan R. (2008) Hybrid modelling of long-term carbon reduction scenarios for the UK. Energy Economics, 30 (6), 2947-2963.
[9] Etiope G. & Schwietzke S. (2019) Global geological methane emissions: An update of top-down and bottom-up estimates. Elementa: Science of the Anthropocene, 7: 47. https://doi.org/10.1525/elementa.383.
[10] Bottom-Up and Top-Down Approaches for National MRV Systems. (2018) UNDP’s NDC Support Programme is funded by the European Union and the governments of Germany and Spain as a contribution to the NDC Partnership.
[11] MRV in Practice -connecting Bottom-Up and Top-Down Approaches for developing National MRV systems for NDCS. (2018), NDC Support Programme.
[12] Yoon Hee Kim, Sting F. J. & C. H. Loch C. H. (2014) Top-Down, Bottom-Up, or Both? Toward an Integrative Perspective on Operations Strategy Formation In Press, Journal of Operations Management. DOI: 10.1016/j.jom.2014.09.005.
[13] Crespi V., Galstyan A. & Lerman K. Top-down vs bottom-up methodologies in multi-agent system design., Reasech Gate. DOI: 10.1007/s10514-007-9080-5.
[14] P. M. Swamidass P. M., Darlow N. & Baines T. (2001) Evolving Forms of Manufacturing Strategy Development: Evidence and Implications. International Journal of Operations & Production Management, 21, 1289-1304.
[15] Kulmer V. (2012) Directed Technological Change in a Bottom-Up/Top-Down CGE model: Analysis of Passenger Transport. Ecomod Conference Paper, [online]. Available: ecomod.net>system>files>Kulmer_Veronika_Direct.
[16] Yin R. K. (2009) Case Study Reserach: Design and Methods. 4th ed., Sage, Thousand Oaks, CA.
[17] Ammann P. & Offutt J. (2008) Introduction to Software Testing. Cambridge University Press, New York.
[18] Rutherford T. F. (2005) Integrating Bottom-Up into Top-Down: A Mixed Complementarity Approach. Discussion Paper No. 05-28, ZEW, Mannheim.
[19] Martinsen T. (2011) Introducing technology learning for energy technologies in a national CGE model through soft links to global and national energy models. Energy Policy, 39 (6), 3327-3336.
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  • APA Style

    Kulyk Mykhailo. (2021). Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics. American Journal of Electrical and Computer Engineering, 5(1), 25-31. https://doi.org/10.11648/j.ajece.20210501.14

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    ACS Style

    Kulyk Mykhailo. Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics. Am. J. Electr. Comput. Eng. 2021, 5(1), 25-31. doi: 10.11648/j.ajece.20210501.14

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    AMA Style

    Kulyk Mykhailo. Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics. Am J Electr Comput Eng. 2021;5(1):25-31. doi: 10.11648/j.ajece.20210501.14

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  • @article{10.11648/j.ajece.20210501.14,
      author = {Kulyk Mykhailo},
      title = {Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics},
      journal = {American Journal of Electrical and Computer Engineering},
      volume = {5},
      number = {1},
      pages = {25-31},
      doi = {10.11648/j.ajece.20210501.14},
      url = {https://doi.org/10.11648/j.ajece.20210501.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajece.20210501.14},
      abstract = {The TD-BU methodology covers a wide range of objects of various "physical" nature and with various analysis tasks. The feature of such objects is that they have a hierarchical structure. Mathematically, they are related by the formalization of upper-level processes by algebraic equations, while lower levels are described by means of mathematical programming. Currently being extensively researched the forecast status of ultra-large hierarchical systems such as "the country's economy - its fuel and energy complex" with certain requirements. The excessive dimensions of such systems create difficulties in their analysis in the classical formulation, so most researchers use diacoptic methods and therefore these tasks TD-BU are labor-intensive. There are a large number of objects to which the TD-BU methodology could be formally applied. We are talking, among other things, about forecasting the volume of production of all types of products, services and demand for them what is necessary for the activities of all sectors of the economy with details at hierarchical levels. For the tasks of this type the key is the problem of discrepancy of the upper and lower levels indicators. This problem cannot be solved by existing TD-BU models. This paper presents a mathematical model and methods for analytical determination of indicators of the upper and lower levels in the above problems, which solve the problem of ambiguity. The mathematical model is formed in such a way that provides an opportunity to find solutions for the upper and each of the lower (sectoral) levels in a unique, analytical form. Therefore, the search for solutions is non-iterative and not laborious. It is carried out in two stages. On the first of them, using known (standard) methods, forecasts are developed for preliminary indicators of the upper and lower levels. At the second stage a special system of algebraic equations is formed, from which analytical dependences for calculation of refined indicators of both levels are defined. This ensures a complete match between the upper indicator and the sum of the lower levels indicators, which is demonstrated by the example of forecasting electricity demand. These mathematical models and methods can also be used to reconcile the reporting indicators of the upper and lower levels of the respective objects (management structures, banks, trade network, etc.). Thus the coordinated decisions are formed in one stage.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Top-Down and Bottom-Up Solutions Within One Mathematical Model on the Example of Energetics
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    JF  - American Journal of Electrical and Computer Engineering
    JO  - American Journal of Electrical and Computer Engineering
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Author Information
  • Institute of General Energy NAS of Ukraine, Kyiv, Ukraine

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