Skip to main content
SpringerLink
Log in

Solution approach to infinite linear programming problem with capacity constraints

  • Research Paper
  • Published:
4OR Aims and scope Submit manuscript

Abstract

The purpose of this article is to investigate a kind of infinite linear programming problem (ILPP) arising from infinite multiclass network equilibrium problems. In several cases, we construct special feasible solutions to the ILPP. By virtue of the nature of network, we prove that the solutions are optimal. Marcotte and Zhu (Oper Res Lett 37:211–214, 2009) proved the existence of the valid tolls for the infinite multiclass network equilibrium problems. Based on this, we analyze the property of the tolls vector, i.e., the relationship between breakpoints and the tolls. We also consider the solutions in the network where origin-destination pairs may differ in their probability density functions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Daniele P, Giuffrè S, Maugeri A (2009) Remarks on general infinite dimensional duality with cone and equality constraints. Commun Appl Anal 13(4): 567–578

    Google Scholar 

  • Daniele P, Maugeri A, Oettli W (1999) Time-dependent traffic equilibria. J Optim Theor Appl 103(3): 543–555

    Article  Google Scholar 

  • Dial RB (1996) Bicriterion traffic assignment: basic theory and elementary algorithms. Transp Sci 30: 93–111

    Article  Google Scholar 

  • Dial RB (1997) Bicriterion traffic assignment: efficient algorithms plus examples. Transp Res B 31: 357–379

    Article  Google Scholar 

  • Dial RB (1999a) Network-optimized road pricing: part I: a parable and a model. Oper Res 47: 54–64

    Article  Google Scholar 

  • Dial RB (1999b) Network-optimized road pricing: part II: algorithms and examples. Transp Sci 47: 327–336

    Google Scholar 

  • Larsson T, Patriksson M (1999) Side constrained traffic equilibrium models-analysis. computation and applications. Transp Res B 33: 233–264

    Article  Google Scholar 

  • Leurent F (1993) Cost versus time equilibrium over a network. Eur J Oper Res 71: 205–221

    Article  Google Scholar 

  • Marcotte P, Zhu DL (1997) Equilibria with infinitely many differentiated classes of customers. In: Pang JS, Ferris M (eds) Complementarity and variational problems-state of the art. SIAM, Philadelphia, pp 234–258

    Google Scholar 

  • Marcotte P, Zhu DL (2009) Existence and computation of optimal tolls in multiclass network equilibrium problems. Oper Res Lett 37: 211–214

    Article  Google Scholar 

  • Yang H, Huang HJ (2004) The multi-class, multi-criteria traffic network equilibrium and systems optimum problem. Transp Res B 38: 1–15

    Article  Google Scholar 

Download references

Author information

Author notes

  1. QingJi Yang

    Present address: Department of Applied Mathematics, Shanghai Finance University, No. 995, Shangchuan Road, Pudong New Area, Shanghai, 201209, People’s Republic of China

Authors and Affiliations

  1. School of Management, Fudan University, Shanghai, 200433, People’s Republic of China

    QingJi Yang

Authors
  1. QingJi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to QingJi Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Q. Solution approach to infinite linear programming problem with capacity constraints. 4OR-Q J Oper Res 9, 261–277 (2011). https://doi.org/10.1007/s10288-011-0155-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-011-0155-y

Keywords

MSC classification (2000)

Search

Navigation