Skip to main content
SpringerLink
Log in

Extremization of multi-objective stochastic fractional programming problem

An application to assembled printed circuit board problem

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

Abstract

This paper addresses classes of assembled printed circuit boards, which faces certain kinds of errors during its process of manufacturing. Occurrence of errors may lead the manufacturer to be in loss. The encountered problem has two objective functions, one is fractional and the other is a non-linear objective. The manufacturers are confined to maximize the fractional objective and to minimize the non-linear objective subject to stochastic and non-stochastic environment. This problem is decomposed into two problems. A solution approach to this model has been developed in this paper. Results of some test problems are provided.

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

  • Charles, V., D. Dutta, and K. Appal Raju. (2001). “Linear Stochastic Fractional Programming Problem.” In Bani Singh, U.S. Gupta, G.S. Stivastava, T.R. Gulati, and V.K. Katiyar (eds.), Proceedings of International Conference on Mathematical Modelling: New Delhi: Tata McGraw-Hill Publishing Ltd.

    Google Scholar 

  • Charles, V., and D. Dutta. (2001). “Linear Stochastic Fractional Programming with Branch-and-Bound Technique.” In R. Nadarajan, and P.R. Kandasamy (eds.), Proceedings of National Conference on Mathematical and Computational Models: Chennai: Allied Publishers Ltd.

    Google Scholar 

  • Charles, V., and D. Dutta. (2003). “Bi-Weighted Multi-Objective Stochastic Fractional Programming Problem with Mixed Constraints.” In R. Nadarajan, and G. Arulmozhi (eds.), Proceedings of Second National Conference on Mathematical and Computational Models: Chennai: Allied Publishers Ltd.

    Google Scholar 

  • Charnes, A., and W.W. Cooper. (1954). “Chance Constrained Programming.” Management Science 6.

  • Charnes, A., and W.W. Cooper. (1962). “Programming with Linear Fractional Functions.” Naval Research Logistic Quarterly 9, 181–186.

    Google Scholar 

  • Cheney, E.W., and A.A. Goldstein. (1959). “Newton's Method of Convex programming and Tchebycheff Approximation.” Numerische Methematik 1, 253–268.

    Article  Google Scholar 

  • Dutta, D., J.R. Rao, and R.N. Tiwari. (1993). “A Restricted Class of Multi Objective Linear Fractional Programming Problems.” European Journal of Operational Research 68, 352–355.

    Article  Google Scholar 

  • Eschenauer, H., J. Koshi, and A. Osyczka. (1990). Multicriteria Design Optimization Procedures and Applications. New York: Springer Verlag.

    Google Scholar 

  • Gupta, S.N., and Kanti Swarup. (1979). “Stochastic Fractional Functionals Programming.” Ricerca Operativa, Franco Angeli-anno IX-nuova Serien 10, 65–78.

    Google Scholar 

  • Gupta, S.N., Kanti Swarup, and Banwarilal. (1981). “Stochastic Fractional Programming with Random Technology Matrix.” Gujarat Statistical Review VIII, 23–34.

    Google Scholar 

  • Im Stancu-Minasian, and M.J. Wets. (1976). A Research Bibliography in Stochastic Programming 1955–1975: CORE Discussion Papers 7603. Belgium: University Catholique de Louvain.

    Google Scholar 

  • Im Stancu-Minasian. (1977). Bibliography of Fractional Programming 1960–1976. Preprint nr.3, Department of Economic Cybemetics, Bucharest: ASE.

    Google Scholar 

  • Jeeva, M., R. Rajalakshmi, and V. Charles. (2002). “Stochastic Programming in Manpower Planning—Cluster Based Optimum Allocation of Recruitments.” In J.R. Artalejo, and A. Krishnamoorthy (eds.), Advances in Stochastic Modelling: New Jersey: USA: Notable Publications, Inc.

    Google Scholar 

  • Jeeva, M., R. Rajalakshmi, V. Charles, and V.S.S. Yadavalli. (2004). “An Application of Stochastic Programming with Weibull Distribution—Cluster Based Optimum Allocation of Recruitments in Manpower Planning.” Journal of Stochastic Analysis and Applications 22 (3), 801–812.

    Article  Google Scholar 

  • Kelly, J.E. (1960). “The Cutting Plane for Solving Convex Programs.” Journal of SIAM VIII (4), 703–712.

    Google Scholar 

  • Martel, A., and W. Price. (1981). “Stochastic Programming Applied to Human Resource Planning.” North Holland: Operational Research Society 32, 187–196.

    Article  Google Scholar 

  • Rao, S.S. (1984). “Multiobjective Optimization in Structural Design in the Presence of Uncertain Parameters and Stochastic Process.” AIAA Journal 22, 1670–1678.

    Article  Google Scholar 

  • Rao, S.S., and H.R. Eslampour. (1986). “Multistage Multiobjective Optimization of Gearboxes.” ASME Journal of Mechanisms, Transmissions & Automation in Design 108, 461–468.

    Article  Google Scholar 

  • Zionts, S. (1968). “Programming with Linear Fractional Functionals.” Naval Research Logistic Quarterly 15, 449–451.

    Google Scholar 

  • http://users.iems.nwu.edu/jrbirge/html/dholmes/SPTSlists.html.

  • http://mally.eco.rug.nl/biblio/Splist.html.

Download references

Author information

Authors and Affiliations

  1. Department of Management Science, SDM Institute for Management Development, Karnataka, Mysore, INDIA, 570 011

    V. Charles

  2. Department of Mathematics & Humanities, National Institute of Technology Warangal, Andhra Pradesh, INDIA, 506 004

    D. Dutta

Authors
  1. V. Charles
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Charles.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Charles, V., Dutta, D. Extremization of multi-objective stochastic fractional programming problem. Ann Oper Res 143, 297–304 (2006). https://doi.org/10.1007/s10479-006-7389-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-006-7389-7

Keywords

Search

Navigation