Skip to main content
SpringerLink
Log in

Linear programming with stochastic processes as parameters as applied to production planning

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

Abstract

In formulating stochastic programming with recourse models, the parameters of the linear programs are usually assumed to be random variables with known distributions. In this paper, the requirement vector parameter is assumed to be a stochastic process {ξ i (t),t∈T,i=1,...,m}. The properties of the deterministic equivalents for the cases of the discrete and continuous index setT are derived. The results of the paper are applied to a multi-item production planning model with continuous (periodic) review of the stock on hand of various items.

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. A. Charnes and W.W. Cooper, Chance-constrained programming, Manag. Sci. 6 (1959) 73–79.

    Google Scholar 

  2. D.R. Cox and H.D. Miller,The Theory of Stochastic Processes, (Wiley, New York, 1968).

    Google Scholar 

  3. G.B. Dantzig, Linear programming under uncertainty, Manag. Sci. 1 (1955) 197–206.

    Google Scholar 

  4. J.L. Folks and R.S. Chikara, The inverse Gaussian distribution and its statistical applications —a review, J. Roy. Statist. Soc. B 40 (1978) 263–275.

    Google Scholar 

  5. R. Jagannathan, Use of sample information in stochastic recourse and chance-constrained programming models, Manag. Sci. 31 (1985) 96–108.

    Google Scholar 

  6. P. Kall,Stochastic Linear Programming (Springer, New York, 1976).

    Google Scholar 

  7. S.M. Ross,Stochastic Processes (Wiley, New York, 1983).

    Google Scholar 

  8. M. Simmonard,Linear Programming (Prentice-Hall, Englewood Cliffs, 1966).

    Google Scholar 

  9. R.J.B. Wets, Programming under uncertainty: the equivalent convex program, SIAM J. Appl. Math. 14 (1966) 89–105.

    Google Scholar 

  10. R.J.B. Wets, Stochastic programming: solution techniques and approximation schemes, in:Mathematical Programming, The State-of-the-Art, eds. A. Bachem, M. Grotschel and B. Korte, (Springer, Berlin, 1982) pp. 566–603.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Science, The University of Iowa, 52242, Iowa City, IA, USA

    Raj Jagannathan

Authors
  1. Raj Jagannathan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jagannathan, R. Linear programming with stochastic processes as parameters as applied to production planning. Ann Oper Res 30, 107–114 (1991). https://doi.org/10.1007/BF02204812

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02204812

Keywords

Search

Navigation