Skip to main content
SpringerLink
Log in

Revealed Preference for Network Design in Bilevel Linear Programming

  • Conference paper
  • First Online:
Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11471))

  • 625 Accesses

Abstract

We study the aggregation of user preferences in the network flow model. These users can be referred to the followers in the sequential decision model. We transform the preference data revealed by the followers into a bundle of linear constraints to represent the strategic norms of the followers in the centralized decision model. We also show that the revealed preference theory is a useful foundation to construct such a multiple users’ rational norm without losing much the richness of preference by our simplification. Although the aggregated preference results in a set of ambiguous decision norms of the representative follower, in our case a convex polyhedron, we can apply this framework to the bilevel optimization and formulate this sequential decision problem as a maximin problem which is the centralized decision problem of the leader in our network flow model.

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

References

  1. Afriat, S.N.: The construction of utility functions from expenditure data. Int. Econ. Rev. 8(1), 67 (1967)

    MATH  Google Scholar 

  2. Bard, J.F.: Coordination of a multidivisional organization through two levels of management. Omega 11(5), 457–468 (1983)

    Google Scholar 

  3. Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht (1998)

    MATH  Google Scholar 

  4. Bazaraa, M.S., Jarvis, J.J.: Linear Programming and Network Flows. Wiley, New York (1977)

    MATH  Google Scholar 

  5. Ben-Ayed, O., Blair, C.E., Boyce, D.E., LeBlanc, L.J.: Construction of a real-world bilevel linear programming model of the highway network design problem. Ann. Oper. Res. 34(1), 219–254 (1992)

    MathSciNet  MATH  Google Scholar 

  6. Bialas, W.F., Karwan, M.H.: On two-level optimization. IEEE Trans. Autom. Control 27(1), 211–214 (1982)

    MATH  Google Scholar 

  7. Calvete, H.I., Galé, C.: Linear bilevel programming with interval coefficients. J. Comput. Appl. Math. 236(15), 3751–3762 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Chambers, C.P., Echenique, F.: Revealed Preference Theory. Econometric Society Monographs, vol. 56. Cambridge University Press, Cambridge (2016)

    MATH  Google Scholar 

  9. Christiansen, S., Patriksson, M., Wynter, L.: Stochastic bilevel programming in structural optimization. Struct. Multi. Optim. 21(5), 361–371 (2001)

    Google Scholar 

  10. Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic, Dordrecht (2002)

    MATH  Google Scholar 

  11. Inuiguchi, M., Sariddichainunta, P.: Bilevel linear programming with ambiguous objective function of the follower. Fuzzy Optim. Decis. Making 15(4), 415–434 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Islam, S.M.N.: Mathematical Economics of Multi-level Optimisation: Theory and Application. Physica, Heidelberg (1998)

    Google Scholar 

  13. LeBlanc, L.J., Boyce, D.E.: A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transp. Res. Part B Methodol. 20(3), 259–265 (1986)

    MathSciNet  Google Scholar 

  14. Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, New York (1995)

    MATH  Google Scholar 

  15. Migdalas, A.: Bilevel programming in traffic planning: models, methods and challenge. J. Global Optim. 7(4), 381–405 (1995)

    MathSciNet  MATH  Google Scholar 

  16. Patriksson, M.: On the applicability and solution of bilevel optimization models in transportation science: a study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints. Transp. Res. Part B Methodol. 42(10), 843–860 (2008)

    Google Scholar 

  17. Ren, A., Wang, Y.: A cutting plane method for bilevel linear programming with interval coefficients. Ann. Oper. Res. 223(1), 355–378 (2014)

    MathSciNet  MATH  Google Scholar 

  18. Ruzíyeva, A., Dempe, S.: Yager ranking index in fuzzy bilevel optimization. Artif. Intell. Res. 2(1), 55 (2012)

    Google Scholar 

  19. Sariddichainunta, P., Inuiguchi, M.: Bilevel linear programming with lower-level fuzzy objective function. In: 2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS), pp. 1–6 (2017)

    Google Scholar 

  20. Sariddichainunta, P., Inuiguchi, M.: The improvement of optimality test over possible reaction set in bilevel linear optimization with ambiguous objective function of the follower. J. Adv. Comput. Intell. Intell. Inform. 19(5), 645–654 (2015)

    Google Scholar 

  21. Sariddichainunta, P., Inuiguchi, M.: Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function. Ann. Oper. Res. 256(2), 285–304 (2017)

    MathSciNet  MATH  Google Scholar 

  22. von Stackelberg, H.: Market Structure and Equilibrium. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-12586-7. (Translated by Bazin, D., Hill, R., Urch, L.)

    MATH  Google Scholar 

  23. Varian, H.R.: Revealed preference and its applications. Econ. J. 122(560), 332–338 (2012)

    Google Scholar 

  24. Williams, H.P.: Model Building in Mathematical Programming, 5th edn. Wiley, Chichester (2013)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    Puchit Sariddichainunta & Masahiro Inuiguchi

Authors
  1. Puchit Sariddichainunta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masahiro Inuiguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Puchit Sariddichainunta .

Editor information

Editors and Affiliations

  1. Osaka University, Toyonaka, Osaka, Japan

    Hirosato Seki

  2. Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan

    Canh Hao Nguyen

  3. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  4. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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

Sariddichainunta, P., Inuiguchi, M. (2019). Revealed Preference for Network Design in Bilevel Linear Programming. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-14815-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14814-0

  • Online ISBN: 978-3-030-14815-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation