Skip to main content
SpringerLink
Log in

On an Applied Problem of Vector Optimization

  • Conference paper
  • First Online:
Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

  • 574 Accesses

Abstract

The paper is devoted to the construction and investigation of mathematical models of economic processes in a local product market. The problem of optimization of prices at outlets of an autonomous network of wholesale under additional restrictions is in focus. The mathematical model of this problem belongs to the class of linear problems of vector optimization. The main properties of the multicriteria problem are studied. An optimal plan is defined. The necessary and sufficient conditions for optimality are established. The theorem of the existence and uniqueness of the optimal plan is formulated. A finite iterative procedure for the problem solution is developed on the base of the obtained theoretical results. The suggested numerical algorithm is based on specific variations of model parameters. The results are illustrated by examples of numerical solutions of some intuitive economic problems with using model data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Arrow, K., Debreu, G.: Existence of an eguilibrium for a completive economy. Econometrica 22, 256–290 (1954)

    Google Scholar 

  2. Asanov, M.: Discrete Optimization. UralSCIENCE, Ekaterinburg (1988)

    Google Scholar 

  3. Charnes, A., Cooper, W.: Management Models and Industrial Applications of Linear Programming, vol. 1. Wiley, New York (1961)

    MATH  Google Scholar 

  4. Doumpos, M., Zopounidis, C.: Multicriteria Analysis in Finance. SOR. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-05864-1

    Book  MATH  Google Scholar 

  5. Ehrgott, M., Puerto, J., Rodríguez-Chía, A.M.: Primal-dual simplex method for multiobjective linear programming. J. Optim. Theory Appl. 134(3), 483–497 (2007). https://doi.org/10.1007/s10957-007-9232-y

    Article  MathSciNet  MATH  Google Scholar 

  6. Ehrgott, M.: Multicriteria Optimization. Springer, Heidelberg (2005). https://doi.org/10.1007/3-540-27659-9

    Book  MATH  Google Scholar 

  7. Evans, J., Steuer, R.: A revised simplex method for multiple objective programs. Math. Program. 5(1), 54–72 (1973)

    Article  MathSciNet  Google Scholar 

  8. Ginchev, I., Guerraggio, A., Rocca, M.: From scalar to vector optimization. Appl. Math. 51(1), 5–36 (2006). https://doi.org/10.1007/s10492-006-0002-1

    Article  MathSciNet  MATH  Google Scholar 

  9. Hamel, A., Lohne, A., Rudloff, B.: Benson type algorithms for linear vector optimization and applications. J. Optim. Theory Appl. 59(4), 811–836 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Intriligator, M.: Mathematical Optimization and Economic Theory. Prentice-Hall Inc., Englewood Cliffs (1971)

    MATH  Google Scholar 

  11. Johannes, J.: Vector Optimization, Theory, Applications, and Extensions. Springer-Verlag, Heidelberg (2011). https://doi.org/10.1007/978-3-642-17005-8

    Book  MATH  Google Scholar 

  12. Kandoba, I., Kotelnik, K., Uspenskii, A.: On one problem of vector optimization of pricing in an autonomous wholesale market, pp. 1–21. Interim report IR-04-026, IIASA, May 2004. http://pure.iiasa.ac.at/id/eprint/7420/1/IR-04-026.pdf

  13. Koopmans, T.: Analysis of production as an efficient combination of activities. In. Activity Analysis of Production and Allocation, pp. 33–97 (1951)

    Google Scholar 

  14. Lohne, A.: Vector Optimization with Infimum and Supremum. Vector Optimization. Springer Science+Business Media, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18351-5

    Book  MATH  Google Scholar 

  15. Nogin, V.: Multi-criteria decision making. UTAS, S. Peterburg (2007)

    Google Scholar 

  16. Rudloff, B., Ulus, F., Vanderbei, R.: A parametric simplex algorithm for linear vector optimization problems. Math. Program. 163, 213–242 (2017)

    Article  MathSciNet  Google Scholar 

  17. Ruzika, S., Wiecek, M.M.: Approximation methods in multiobjective programming. J. Optim. Theory Appl. 126(3), 473–501 (2005)

    Article  MathSciNet  Google Scholar 

  18. Steuer, R.: Multiple Criteria Optimization: Theory, Computation and Application. Wiley, New York (1986)

    MATH  Google Scholar 

  19. Vasilyev, F.: Metody optimizacii [Optimization Methods]. Faktorial Press, Moscow (2002)

    Google Scholar 

  20. Walras, L., Jaffe, W.: Elements of Pure Economics, or The Theory of Social Wealth. Richard D. Irwin Inc., Homewood (1954). American Economic Association and the Royal Economic Society

    Google Scholar 

  21. Wierzbicki, A.: Reference point methods in vector optimization and decision support, pp. 1–40. Interim report IR-98-017, IIASA, April 1998. http://pure.iiasa.ac.at/id/eprint/5631/1/IR-98-017.pdf

Download references

Author information

Authors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

    Igor Kandoba & Alexander Uspenskii

  2. Institute of Natural Sciences and Mathematics, Ural Federal University named after the first President of Russia B. N. Yeltsin, Ekaterinburg, Russia

    Igor Kandoba & Alexander Uspenskii

Authors
  1. Igor Kandoba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Uspenskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Igor Kandoba .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kandoba, I., Uspenskii, A. (2019). On an Applied Problem of Vector Optimization. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-33394-2_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation