Published January 31, 2020 | Version v1
Journal article Open

ALGORITHM FOR SOLVING THE INVERSE PROBLEMS OF ECONOMIC ANALYSIS IN THE PRESENCE OF LIMITATIONS

Creators

  • 1. Tomsk state university of control systems and radioelectronics

Description

The solution of inverse problems is considered taking into account the restrictions using inverse calculations. An algorithm is proposed for solving the inverse problem, taking into account restrictions while minimizing the sum of the absolute values of the changes in the arguments. The problem of determining the increments of the function arguments is presented as a linear programming problem. The algorithm includes solving the inverse problem with the help of inverse calculations while minimizing the sum of the absolute changes in the arguments, checking the correspondence of the obtained arguments to the given restrictions, adjusting the value of the argument if it goes beyond the limits of acceptable values, and changing the varied arguments to achieve the given value of the resulting indicator. The solution of two problems with the additive and mixed dependence between the arguments of the function is considered. It is shown that the solutions obtained in this case are consistent with the result of using an iterative procedure based on changing the resulting value to a small value until a given result is achieved, and the results are compared with solving problems using the MathCad mathematical package. The advantage of the algorithm is a smaller number of iterations compared to the known method, as well as the absence of the need to use coefficients of relative importance. The presented results can be used in management decision support systems

Files

ALGORITHM FOR SOLVING THE INVERSE PROBLEMS OF ECONOMIC ANALYSIS IN THE PRESENCE OF LIMITATIONS.pdf

Files (420.7 kB)

Additional details

References

  • Colton, D., Engl, H. W., Louis, A. K., McLaughlin, J. R., Rundell, W. (Eds.) (2000). Surveys on Solution Methods for Inverse Problems. Springer. doi: https://doi.org/10.1007/978-3-7091-6296-5
  • Ekeland, I., Djitté, N. (2006). An inverse problem in the economic theory of demand. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 23 (2), 269–281. doi: https://doi.org/10.1016/j.anihpc.2005.10.001
  • Barbagallo, A., Mauro, P. (2014). An Inverse Problem for the Dynamic Oligopolistic Market Equilibrium Problem in Presence of Excesses. Procedia - Social and Behavioral Sciences, 108, 270–284. doi: https://doi.org/10.1016/j.sbspro.2013.12.837
  • Shananin, A. A. (2018). Inverse Problems in Economic Measurements. Computational Mathematics and Mathematical Physics, 58 (2), 170–179. doi: https://doi.org/10.1134/s0965542518020161
  • Klemashev, N. I., Shananin, A. A. (2016). Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting. Journal of Inverse and Ill-Posed Problems, 24 (4). doi: https://doi.org/10.1515/jiip-2015-0015
  • Beck, A., Teboulle, M. (2009). A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences, 2 (1), 183–202. doi: https://doi.org/10.1137/080716542
  • Odintsov, B. Е., Romanov, А. N. (2014). How to create business performance management (BPM) system. Bulletin of the University of Finance, 6, 22–36.
  • Barmina, Е. А., Kvjatkovskaja, I. Yu. (2010). Monitoring the quality of a commercial organization. Structuring indicators. The use of cognitive maps. Bulletin of the Astrakhan State Technical University, 2, 15–20.
  • Blumin, S. L., Borovkova, G. S. (2018). Application of analysis of finite fluctuations and reverse computations in control systems and decision support systems. Control Sciences, 6, 29–34. doi: https://doi.org/10.25728/pu.2018.6.4
  • Borshchuk, I. V., Odintsov, B. E., Shkvir, V. D. (2013). Inverse calculations in prevent crisis phenomenon of socio-economic systems. International conference on application of information and communication technology and statistics in economy and education. Bulgaria, 140–143.
  • Dik, V. V., Urintsov, A. I., Odintsov, B. Ye., Churikanova, O. Yu. (2014). Decision support methods in balanced ScoreCard. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, 4, 120–126.
  • Ali, H. A. E. M., Al-Sulaihi, I. A., Al-Gahtani, K. S. (2013). Indicators for measuring performance of building construction companies in Kingdom of Saudi Arabia. Journal of King Saud University - Engineering Sciences, 25 (2), 125–134. doi: https://doi.org/10.1016/j.jksues.2012.03.002
  • Gribanova, E. B. (2018). Methods for solving inverse problems of economic analysis by minimizing argument increments. Proceedings of Tomsk State University of Control Systems and Radioelectronics, 21 (2), 95–99. doi: https://doi.org/10.21293/1818-0442-2018-21-2-95-99
  • Gribanova, E. (2019). Development of a price optimization algorithm using inverse calculations. Eastern-European Journal of Enterprise Technologies, 5 (4 (101)), 18–25. doi: https://doi.org/10.15587/1729-4061.2019.180993
  • Odincov, B. E., Romanov, A. N. (2014). Iterative method of optimization of enterprise management by means of inverse calculations. Bulletin of the Financial University, 2, 60–73.
  • Gribanova, E. B. (2016). Stochastic algorithms to solve the economic analysis inverse problems with constraints. Proceedings of Tomsk State University of Control Systems and Radioelectronics, 19 (4), 112–116. doi: https://doi.org/10.21293/1818-0442-2016-19-4-112-116
  • Vanderbei, R. J. (2014). Linear programming. Foundations and Extensions. Springer. doi: https://doi.org/10.1007/978-1-4614-7630-6
  • Ganicheva, A. V. (2019). Method of the solution of some classes optimising tasks. Modeling, optimization and information technology, 7 (2), 43–54. doi: https://doi.org/10.26102/2310-6018/2019.25.2.002
  • Trunov, A. (2015). Modernization of means for analyses and solution of nonlinear programming problems. Quantitative Methods in Economics, XVI (2), 133–141.
  • Shen, B., Shen, Y., Ji, W. (2019). Profit optimization in service-oriented data market: A Stackelberg game approach. Future Generation Computer Systems, 95, 17–25. doi: https://doi.org/10.1016/j.future.2018.12.072
  • O'Neill, B., Sanni, S. (2018). Profit optimisation for deterministic inventory systems with linear cost. Computers & Industrial Engineering, 122, 303–317. doi: https://doi.org/10.1016/j.cie.2018.05.032