IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2779-d881285.html
   My bibliography  Save this article

Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

Author

Listed:
  • Ekaterina Gribanova

    (Faculty of Control Systems, Tomsk State University of Control Systems & Radioelectronics, 40, Lenina Str., 634050 Tomsk, Russia)

Abstract

One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.

Suggested Citation

  • Ekaterina Gribanova, 2022. "Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics," Mathematics, MDPI, vol. 10(15), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2779-:d:881285
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2779/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2779/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dai, Zhifeng & Wen, Fenghua, 2018. "Some improved sparse and stable portfolio optimization problems," Finance Research Letters, Elsevier, vol. 27(C), pages 46-52.
    2. Mohammed Al Horani & Mauro Fabrizio & Angelo Favini & Hiroki Tanabe, 2020. "Inverse Problems for Degenerate Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    3. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
    4. Egri, Péter & Kis, Tamás & Kovács, András & Váncza, József, 2014. "An inverse economic lot-sizing approach to eliciting supplier cost parameters," International Journal of Production Economics, Elsevier, vol. 149(C), pages 80-88.
    Full references (including those not matched with items on IDEAS)

    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. Crönert, Tobias & Martin, Layla & Minner, Stefan & Tang, Christopher S., 2024. "Inverse optimization of integer programming games for parameter estimation arising from competitive retail location selection," European Journal of Operational Research, Elsevier, vol. 312(3), pages 938-953.
    2. Wen, Fenghua & Zhao, Cong & Hu, Chunyan, 2019. "Time-varying effects of international copper price shocks on China's producer price index," Resources Policy, Elsevier, vol. 62(C), pages 507-514.
    3. Yang, Cai & Gong, Xu & Zhang, Hongwei, 2019. "Volatility forecasting of crude oil futures: The role of investor sentiment and leverage effect," Resources Policy, Elsevier, vol. 61(C), pages 548-563.
    4. Chen, Rongda & Xu, Jianjun, 2019. "Forecasting volatility and correlation between oil and gold prices using a novel multivariate GAS model," Energy Economics, Elsevier, vol. 78(C), pages 379-391.
    5. Md Fouad Bin Amin & Mohd Ziaur Rehman, 2022. "Asymmetric Linkages of Oil Prices, Money Supply, and TASI on Sectoral Stock Prices in Saudi Arabia: A Non-Linear ARDL Approach," SAGE Open, , vol. 12(1), pages 21582440211, January.
    6. Xiao, Jihong & Zhou, Min & Wen, Fengming & Wen, Fenghua, 2018. "Asymmetric impacts of oil price uncertainty on Chinese stock returns under different market conditions: Evidence from oil volatility index," Energy Economics, Elsevier, vol. 74(C), pages 777-786.
    7. Hongxin Zhao & Lingchen Kong & Hou-Duo Qi, 2021. "Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 853-881, December.
    8. Jihong Xiao & Xuehong Zhu & Chuangxia Huang & Xiaoguang Yang & Fenghua Wen & Meirui Zhong, 2019. "A New Approach for Stock Price Analysis and Prediction Based on SSA and SVM," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 287-310, January.
    9. XiaoLiang Dong & Deren Han & Zhifeng Dai & Lixiang Li & Jianguang Zhu, 2018. "An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 944-961, December.
    10. Lei Wang & Yan Yan & Xiaoteng Li & Xiaosong Chen, 2018. "General Component Analysis (GCA): A new approach to identify Chinese corporate bond market structures," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-18, July.
    11. András Kovács, 2021. "Inverse optimization approach to the identification of electricity consumer models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 521-537, June.
    12. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2022. "Sparsity and stability for minimum-variance portfolios," Risk Management, Palgrave Macmillan, vol. 24(3), pages 214-235, September.
    13. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    14. Dai, Zhifeng & Dong, Xiaodi & Kang, Jie & Hong, Lianying, 2020. "Forecasting stock market returns: New technical indicators and two-step economic constraint method," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    15. Zhifeng Dai & Jie Kang, 2022. "Some new efficient mean–variance portfolio selection models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4784-4796, October.
    16. Xiao, Jihong & Wen, Fenghua & Zhao, Yupei & Wang, Xiong, 2021. "The role of US implied volatility index in forecasting Chinese stock market volatility: Evidence from HAR models," International Review of Economics & Finance, Elsevier, vol. 74(C), pages 311-333.
    17. Catarina Moreira & Emmanuel Haven & Sandro Sozzo & Andreas Wichert, 2018. "Process mining with real world financial loan applications: Improving inference on incomplete event logs," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-31, December.
    18. Songshu Liu, 2022. "Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    19. Dai, Zhifeng & Zhu, Huan & Dong, Xiaodi, 2020. "Forecasting Chinese industry return volatilities with RMB/USD exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    20. Zhujia Yin & Yantuan Yu & Jianhuan Huang, 2018. "Evaluation and evolution of bank efficiency considering heterogeneity technology: An empirical study from China," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.

    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:gam:jmathe:v:10:y:2022:i:15:p:2779-:d:881285. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.