Abstract
The problem of minimising E(X) subject to the constraints X ⩾ 0, P(X ⩾ b) ⩾ a(0 < a < 1) has been considered, where b is a non-negative random variable with continuous probability distribution. A necessary and sufficient condition for randomised decisions to be superior to the non-randomised one has been derived.
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Mukerjee, R. Univariate Stochastic Programming with Random Decision Variable. J Oper Res Soc 33, 957–959 (1982). https://doi.org/10.1057/jors.1982.200
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DOI: https://doi.org/10.1057/jors.1982.200