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Prekopa, A. (1966) On the Probability Distribution of the Optimum of a Random Linear Program. SIAM Journal on Control, 4, 211-222.

has been cited by the following article:

  • TITLE: Some Explicit Results for the Distribution Problem of Stochastic Linear Programming

    AUTHORS: Afrooz Ansaripour, Adriana Mata, Sara Nourazari, Hillel Kumin

    KEYWORDS: Stochastic Linear Programming, The Wait and See Problem, Mathematics Subject Classification

    JOURNAL NAME: Open Journal of Optimization, Vol.5 No.4, December 30, 2016

    ABSTRACT: A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain; indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.