Skip to main content
SpringerLink
Log in

Der gegenwärtige Stand der stochastischen Programmierung

  • Abhandlungen
  • Published:
Unternehmensforschung Aims and scope Submit manuscript

Zusammenfassung

Wenn in einem linearen Programm einige oder alle Koeffizienten Zufallsvariable sind, verliert die Zielsetzung dieses linearen Programmes offenbar ihren Sinn. Die dann auftretenden neuen Problemstellungen, die bisher in der Literatur behandelt wurden, sollen in dieser Arbeit diskutiert werden: Das Verteilungsproblem, das Programm mit Wahrscheinlichkeitsrestriktionen und das zweistufige Problem.

Summary

If in a linear program some (or all) of the coefficients are random variables, the objective of linear programming does obviously not remain meaningful. The new problems arising in this case, which have been considered in the literature, will be discussed in this paper, namely the distribution problem, the program with chance constraints and the stochastic program with recourse (“Two-stage programming”).

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

Literaturverzeichnis

  1. Bereanu, B: On stochastic linear programming I. Revue de mathématiques pures et appliquées 8 (1963), 683–697.

    Google Scholar 

  2. ——: On stochastic linear programming II. Revue Roum. math. pures et appl. 11 (1966), 713–725.

    Google Scholar 

  3. ——: On stochastic linear programming. The Laplace transform of the distribution of the optimum and applications. J. of Mathematical Analysis and Applications 15 (1966), 280–294.

    Google Scholar 

  4. ——: On stochastic linear programming distribution problems, stochastic technology matrix. Z. Wahrscheinlichkeitstheorie verw. Geb. 8 (1967), 148–152.

    Google Scholar 

  5. Charnes, A. andW. W. Cooper: Chance constrained programming. Management Science 6 (1959), 73–79.

    Google Scholar 

  6. —— ——: Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Research 11 (1963), 18–39.

    Google Scholar 

  7. Charnes, A., W. W. Cooper andG. L. Thompson: Constrained generalized medians and hypermedians as deterministic equivalents for two-stage linear programs under uncertainty. Management Science 12 (1965), 83–112.

    Google Scholar 

  8. Charnes, A. andM. J. L. Kirby: Optimal decision rules for theE-model of chance-constrained programming. Cahiers du Centre d'Etudes de Recherche Operationnelle 8 (1966), 5–44.

    Google Scholar 

  9. Dantzig, G. B.: Lineare Programmierung und Erweiterungen. (Deutsche Bearbeitung vonA. Jaeger). Springer, Berlin (1966).

    Google Scholar 

  10. El Agizy, M.: Two-stage programming under uncertainty with discrete distribution function. Operations Research 15 (1967), 55–70.

    Google Scholar 

  11. Elmaghraby, S. E.: An approach to linear programming under uncertainty. Operations Research 7 (1959), 208–216.

    Google Scholar 

  12. Hadley, G.: Nonlinear and dynamic programming. Addison-Wesley. Reading (Mass.) (1964).

    Google Scholar 

  13. Kall, P.: Qualitative Aussagen zu einigen Problemen der stochastischen Programmierung. Z. Wahrscheinlichkeitstheorie verw. Geb. 6 (1966), 246–272.

    Google Scholar 

  14. ——: Das zweistufige Problem der stochastischen linearen Programmierung. Z. Wahrscheinlichkeitstheorie verw. Geb. 8 (1967), 101–112.

    Google Scholar 

  15. ——: Produktionsoptimierung mit Hilfe der stochastischen Programmierung. Industrielle Organisation 36 (1967), 427–432.

    Google Scholar 

  16. Kirby, M. J. L.: The current state of chance constrained programming. Systems Research Memorandum No. 181, Northwestern University, Evanston, Ill. (1967).

    Google Scholar 

  17. Madansky, A.: Inequalities for stochastic linear programming problems. Management Science 6 (1960), 197–204.

    Google Scholar 

  18. ——: Methods of solution of linear programs under uncertainty. Operations Research 10 (1962), 463–471.

    Google Scholar 

  19. Moeseke, P. van, andG. Tintner: Base duality theorem for stochastic and parametric linear programming. Unternehmensforschung 8 (1964), 75–79.

    Google Scholar 

  20. Prékopa, A.: On probabilistic constrained programming. Vortrag am Mathematical Programming Symposium, Princeton University, August 1967.

  21. Sengupta, J. K., G. Tintner andC. Millham: On some theorems of stochastic linear programming with applications. Management Science 10 (1964), 143–159.

    Google Scholar 

  22. Tintner, G.: Stochastic linear programming with applications to agricultural economics. Proc. 2nd Sympos. Lin. Programming (H. Antosiewicz, ed.), Washington, D. C. (1955).

  23. Tintner, G., C. Millham andJ. K. Sengupta: A weak duality theorem for stochastic linear programming. Unternehmensforschung 7 (1963), 1–8.

    Google Scholar 

  24. Van Slike, R. andR. Wets: Programming under uncertainty and stochastic optimal control. J. SIAM Control 4 (1966), 179–193.

    Google Scholar 

  25. Walkup, D. W. andR. Wets: Stochastic programs with recourse. Boeing Document D 1-82-0551, Boeing Scientific Research Laboratories, Seattle, Washington (1966).

    Google Scholar 

  26. Wets, R.: Programming under uncertainty: The complete problem. Z. Wahrscheinlichkeits-theorie verw. Geb. 4 (1966), 316–339.

    Google Scholar 

  27. ——: Programming under uncertainty: The equivalent convex program. J. SIAM Appl. Math. 14 (1966), 89–105.

    Google Scholar 

  28. ——: Programming under uncertainty: The solution set. J. SIAM Appl. Math. 14 (1966), 1143–1151.

    Google Scholar 

  29. Williams, A. C.: On stochastic linear programming. J. SIAM Appl. Math. 13 (1965), 927–940.

    Google Scholar 

  30. ——: Approximation formulas for stochastic linear programming. J. SIAM Appl. Math. 14 (1966), 668–677.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FIDES Treuhandvereinigung, Bleicherweg 33, Zürich, Schweiz

    P. Kall

Authors
  1. P. Kall
    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

Kall, P. Der gegenwärtige Stand der stochastischen Programmierung. Unternehmensforschung Operations Research 12, 81–95 (1968). https://doi.org/10.1007/BF01918316

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01918316

Search

Navigation