Skip to main content
Log in

On decision rules in stochastic programming

  • Published:
Mathematical Programming Submit manuscript

Abstract

The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms. A liberal dosage of examples is provided which illustrate various cases. The treatment is unified by making use of the equivalence of various formulations which have appeared in the literature. An appendix is devoted to the P-model for stochastic programs with chance constraints.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. D. Blackwell and N.S. Girshick,Theory of games and statistical decisions (Wiley, New York, 1954).

    Google Scholar 

  2. A. Charnes and W.W. Cooper, “Chance-constrained programming”,Management Science 6 (1959) 73–79.

    Google Scholar 

  3. A. Charnes and W.W. Cooper, “Deterministic equivalents for optimizing and satisficing under chance constraints”,Operations Research 11 (1963) 18–39.

    Google Scholar 

  4. A. Charnes and W.W. Cooper, “Chance-constraints and normal deviates”,Journal of the American Statistical Association 52 (1962) 134–148.

    Google Scholar 

  5. A. Charnes, W.W. Cooper and M.J.L. Kirby, “Optimal decision rules in conditional probabilistic programming”,Atti della Accademia Nazionale dei Lincei, Memorie, Classe di Scienze Fisiche, Mathematiche e Naturali, Sezione VIII 45 (1968) 231–235.

    Google Scholar 

  6. A. Charnes, W.W. Cooper and G. Symonds, “Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil production”,Management Science 4 (1958) 235–263.

    Google Scholar 

  7. A. Charnes and M.J.L. Kirby, “Optimal decision rules for the E-model of chance-constrained programming”,Cahiers du Centre d'Etudes de Recherche Operationelle 8 (1966) 5–44.

    Google Scholar 

  8. A. Charnes and M.J.L. Kirby, “Optimal decision rules for the triangular E-model of chance-constrained programming”,Cahiers du Centre d'Etudes de Recherche Operationnelle 12 (1969) 215–243.

    Google Scholar 

  9. A. Charnes and M.J.L. Kirby, “Some special P-models in chance-constrained programming”,Management Science 14 (1967) 183–195.

    Google Scholar 

  10. M.J. Eisner, “On duality in infinite-player games and sequential chance-constrained programming”, Ph.D. Dissertation, Cornell University, Ithaca, N.Y. (1970).

    Google Scholar 

  11. M.J. Eisner, R.S. Kaplan and J.V. Soden, “Admissible decision rules for the E-model of chance-constrained programming”,Management Science 17 (1971) 337–353.

    Google Scholar 

  12. R. Kaplan and J. Soden, “On the objective function for the sequential P-model of chance-constrained programming”,Operations Research 19 (1971) 105–114.

    Google Scholar 

  13. K.O. Kortanek and J.V. Soden, “On the Charnes—Kirby optimality theorem for the conditional chance-constrained E-model”,Cahiers du Centre d'Etudes de Recherche Operationnelle 8 (1967) 78–98.

    Google Scholar 

  14. M. Lane, “A conditional chance constrained model for reservoir control”, Manuscript, London School of Economics (1972).

  15. D. Walkup and R.J.-B. Wets, “Stochastic programs with recourse”,SIAM Journal on Applied Mathematics 15 (1967) 1299–1314.

    Google Scholar 

  16. D. Walkup and R.J.-B. Wets, “Stochastic programs with recourse: Special forms”, in:Proceedings of the Princeton symposium on mathematical programming, Ed. H.W. Kuhn (1970) pp. 139–161.

  17. D. Walkup and R.J.-B. Wets, “A note on decision rules for stochastic programs”,Journal of Computer and System Sciences 2 (1968) 305–311.

    Google Scholar 

  18. D. Walkup and R.J.-B. Wets, “Lifting projections of convex polyhedra”,Pacific Journal of Mathematics 28 (1969) 465–475.

    Google Scholar 

  19. R.J.-B. Wets, “Characterization theorems for stochastic programs with recourse”,Mathematical Programming 2 (1972) 166–175.

    Google Scholar 

  20. W. Ziemba, “Transforming stochastic dynamic programming problems into nonlinear programs”,Management Science 17 (1971) 450–462.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Garstka, S.J., Wets, R.J.B. On decision rules in stochastic programming. Mathematical Programming 7, 117–143 (1974). https://doi.org/10.1007/BF01585511

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585511

Keywords

Navigation