Skip to main content
Log in

The computational complexity of multi-level linear programs

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We show that (L+1)-level linear programs are as difficult as levelL of the polynomial-time hierarchy, even if one only considers problems with unique optimal solutions.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Bard and J. Falk, An explicit solution to the multi-level programming problem, Comput. Oper. Res. 9(1982)77–100.

    Google Scholar 

  2. O. Ben-Ayed and C. Blair, Computational difficulties of bilevel linear programming, Oper. Res. 38(1990)556–559.

    Google Scholar 

  3. W. Candler and R. Norton, Multilevel programming and development policy, World Band Staff Working Paper No. 258, IBRD, Washington, DC (1977).

  4. J. Fortuny-Amat and B. McCarl, Multilevel programming, Department of Agricultural Economics, Purdue University (1979).

  5. M. Garey and D. Johnson,Computers and Intractability (Freeman, San Francisco, 1979).

    Google Scholar 

  6. R. Jeroslow, The polynomial hierarchy and a simple model for competitive analysis, Math. Progr. 32(1985)146–165.

    Google Scholar 

  7. L. Stockmeyer, The polynomial-time hierarchy, Theor. Comput. Sci. 3(1977)1–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Robert Jeroslow (1942–1988)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blair, C. The computational complexity of multi-level linear programs. Ann Oper Res 34, 13–19 (1992). https://doi.org/10.1007/BF02098170

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02098170

Keywords

Navigation