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On the use of computers in planning under conditions of uncertainty

Über die Verwendung von Computern in der Planung mit Unsicherheitsfaktoren

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Abstract

In this paper there are presented some recent results in stochastic linear programming which require for obtaining numerical solutions mainly the existing efficient programs for linear and quadratic programming. It is also shown that for stochastic linear programs with simple randomization the minimum risk solution does not depend on the probability distribution of coefficients and can be obtained by linear programming. The relevance of the results to planning under uncertainty is illustrated and numerical examples and computation experience is reported. All the methods presented can provide numerical results for problems of dimensions met in applications.

Zusammenfassung

Es werden neuere Ergebnisse der stochastischen linearen Programmierung aufgezeigt, die zur Erzielung numerischer Lösungen im wesentlichen die bestehenden wirksamen Programme für die lineare und quadratische Programmierung erfordern. Es wird ferner dargelegt, daß die Lösung mit minimalem Risiko für stochastische lineare Programme mit einfacher Umrechnung auf Zufallszahlen nicht von der Wahrscheinlichkeitsverteilung der Koeffizienten abhängig ist und mittels linearer Programmierung erreichbar ist. Die Relevanz der Ergebnisse für die Planung mit Unsicherheitsfaktoren wird erläutert; ferner werden numerische Beispiele gegeben und über die Erfahrungen in der Berechnung berichtet. Mit allen beschriebenen Methoden lassen sich numerische Ergebnisse für die in der Anwendung auftretenden Dimensionsprobleme gewinnen.

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Authors and Affiliations

  1. Center of Mathematical Statistics, Academiei 14, Bucharest 1, Romania

    B. Bereanu

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  1. B. Bereanu
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Bereanu, B. On the use of computers in planning under conditions of uncertainty. Computing 15, 11–32 (1975). https://doi.org/10.1007/BF02252833

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