On Optimization Model Formulation Using Neural Networks

  • Paweł Gąsiorowski
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 12)


Mathematical programming is a widely used tool in Operational Research. The first — and usually the most difficult — step of problem solving requires formulation of the model: finding the mathematical description of the relationships between decisions and their outcomes. The researcher is faced with the problem of finding the proper functions and their parameters. This kind of problems is dealt with using approximation theory.

The paper presents theorems and assumptions for using neural networks as approximators of functions in formulation of the optimization models Thanks to neural networks’ approximation capabilities the difficulties connected with finding the functional forms of relationships and their parameters can be avoided.

The method of identification of parameters is illustrated with an exemplary application in the area of bank credit portfolio optimization.


Neural Network Hide Layer Layer Functional Loan Portfolio Approximation Capability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bierman, Bonini, Hausman, Quantitative Analysis for Business Decisions, IRWIN, Homewood, 1986Google Scholar
  2. 2.
    Boffey R., Robson G.; Bank Credit Risk Management; Managerial Finance November 1995Google Scholar
  3. 3.
    Charemza W., Deadman D; New Econometrics; PWE; Warszawa; 1997 (in Polish) Google Scholar
  4. 4.
    Galas Z., Nykowski I.,Zólkiewski Z.; Multicirteria programming; PWE; Warsaw, 1987 (in Polish) Google Scholar
  5. 5.
    Gasiorowski P.; Application of Neural Networks as functionals approximators on the example of bank loan portfolio optimization; Badania statutowe 03/S/0070/98 Institute of Econometrics; Warsaw School of Economics; 1998 (in Polish) Google Scholar
  6. 6.
    Gasiorwoski P.; Bi-Referential evaluation of bank loan portfolio with neural networks; Proceedings of the Econometrics Workshop Conference, Warsaw School of Economics Press, Forthcoming, (in Polish) Google Scholar
  7. 7.
    Gasiorowski P., Kaminski B.; On application of neural networks in identification of approximation problem; Badania statutowe 03/S/0016/99 Institute of Econometrics; Warsaw School of Economics; 1999 (in Polish) Google Scholar
  8. 8.
    Grabowski W.; Mathematical programming; PWE; Warszawa; 1980 (in Polish) Google Scholar
  9. 9.
    Hartman E, Keeler J., Kowalski J.; Layered Neural Networks with Gaussian Hidden Units as Universal Approximations; Neural Computation; 2, 1990; p. 210 - 215Google Scholar
  10. 10.
    Hornik K.; Approximation Capabilities of Multilayer Feedforward Networks; Neural Networks; vol 4, 1991; p. 251 - 257Google Scholar
  11. 11.
    Hornik K., Stinchcombe M., White H.; Multilayer feedforward networks are universal approximators; Neural Networks, vol 2., p. 359–366; 1989Google Scholar
  12. 12.
    Knowles T., Management Science Building and Using Models, Irwin 1989Google Scholar
  13. 13.
    Krajewski, Ritzman, Operations Management, Strategy and Analysis,Addison Wesley Publishing Company, 1996, ReadingGoogle Scholar
  14. 14.
    Masters T.; Neural Networks in practice; WNT; Warszawa; 1996 (in Polish) Google Scholar
  15. 15.
    McCulloch W.S, Pitt W.; A logical calculus of ideas immanent in nervous activity; Bulletin of Mathematical Biophysics 5; p 115–123; 1943CrossRefGoogle Scholar
  16. 16.
    Misinska D. Commercial bank accounting, Fundacja Rozwoju Rachunkowosci w Polsce, 1995, Warszawa (in Polish) Google Scholar
  17. 17.
    Modha D. S., Hecht-Nielsen R.; Multilayer Functionals, article in Taylor J. G; Mathematical Approaches to Neural Netowrks; North Holland; Amsterdam; 1993Google Scholar
  18. 18.
    Poggio T., Girosi F.; Networks for approximation and learning; Proc. IEEE; 78, nr 9, 1481–1497;1990CrossRefGoogle Scholar
  19. 19.
    Powell T.; Approximation Theory; ITP.;1980Google Scholar
  20. 20.
    Schroeder R.,Operations Management, Decision Making in the Operations Function, Mc Graw-Hill 1993 New YorkGoogle Scholar
  21. 21.
    Tadeusiewicz R.; Neural networks; Akademicka Oficyna Wydawnicza RM; Warszawa; 1993 (in Polish) Google Scholar
  22. 22.
    Zurada J., Barski M., J@druch W.; Artificial neural networks; PWN; Warszawa; 1996 (in Polish) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Paweł Gąsiorowski
    • 1
  1. 1.Division of Decision Analysis and SupportWarsaw School of EconomicsWarsawPoland

Personalised recommendations