Skip to main content
SpringerLink
Log in

Enumeration technique for solving multi-objective quadratic set-covering problem using goal programming

  • Theory and Methodology
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper an algorithm to solve a multi-objective quadratic set-covering problem is presented. It is based on Goal programming approach with Non-Linear objectives under pre-emptive priority structure. The method is illustrated with the help of an example.

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

  1. Garfinkel, R. S., Nemhauser, G. L. (ed.): Integer programming, Wiley Inter Science Publication, John Wiley (1973)

  2. Roth, R.: Computer solution to minimum cover problem. Oper. Res. 17, 455–465 (1969)

    Article  Google Scholar 

  3. Lemke, C.E., Salkin, H.M., Spielberg, K.: Set covering by single branch enumeration with linear programming subproblem. Oper. Res. 19, 998–1022 (1971)

    Article  Google Scholar 

  4. Bellmore, M., Ratliff, H.D.: Set covering and involutory basis. Manage. Sci. 18, 194–206 (1971)

    Article  Google Scholar 

  5. Chavatal, V.: A greedy heuristic for the set covering problem. Math. Oper. Res. 4, 233–235 (1979)

    Article  Google Scholar 

  6. Balas, E.: Cutting planes from conditional bounds, a new approach set covering. Math Prog Study 12, 19–36 (1980)

    Google Scholar 

  7. Saxena, R.R., Arora, S.R.: Enumeration technique for solving multi-objective linear set covering problem. APZOR 12, 87–97 (1995)

    Google Scholar 

  8. Saxena, R.R., Arora, S.R.: Cutting plane technique for the multiobjective set covering problem with linear fractional objective functions. IJOMAS 14(1), 111–122 (1998)

    Google Scholar 

  9. Charnes, A., Cooper, W.W.: Management models and industrial applications of linear programming, vol. 1 and 2. John Wiley and Sons, New York (1961)

    Google Scholar 

  10. Ijiri, Y.: Management Goals and Accounting for Control. Rand-McNally & Co, Chicago (1965)

    Google Scholar 

  11. Pant, J.C., Shah, S.: Linear approach to linear fractional goal programming. Opsearch 29, 297–304 (1992)

    Google Scholar 

  12. Ghosh, D., Pal, B.B., Basu, M.: Ideal solution of goal programming problems with non-linear objectives. IJOMAS 8(1), 19–33 (1992)

    Google Scholar 

  13. Ignizio, J.P.: Goal programming and extensions. Lexington Books, Massachusetts (1976)

    Google Scholar 

Download references

Acknowledgement

We are thankful to the referee for their valuable suggestions which are incorporated in the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Hans Raj College University of Delhi, Delhi, 110007, India

    S. R. Arora & Neelam Malhotra

  2. Department of Mathematics, G. L. A. College, N. P. University, Daltonganj, 822102, Jharkhand, India

    Ravi Shanker

Authors
  1. S. R. Arora
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ravi Shanker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Neelam Malhotra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ravi Shanker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arora, S.R., Shanker, R. & Malhotra, N. Enumeration technique for solving multi-objective quadratic set-covering problem using goal programming. OPSEARCH 48, 20–29 (2011). https://doi.org/10.1007/s12597-011-0038-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-011-0038-1

Keywords

Search

Navigation