Abstract
<jats:p><p>Stochastic programming mathematical models are used in a wide range of problem settings that consider the influence of random factors of various natures. If a loss function dependent on strategy and random parameters is used to describe the system's operation, the value of the loss function becomes random. The quantile criterion utilizes the concept of a quantile function&mdash;the smallest value of the loss function that will not be exceeded with a probability no lower than a specified value. Thus, reliability is limited to an acceptable level, and the effectiveness of strategy implementation is optimized. The original problem can be reduced to a minimax problem, where the maximum is taken over the confidence set proposed to be optimized (the so-called confidence method). Using the confidence method, the original problem is approximated by a deterministic minimax problem parameterized by the radius of a sphere inscribed in the polyhedral confidence set. The author's previously proposed algorithm for solving a two-stage facility location problem with a quantile criterion and choice of reliability level has been generalized to the case of an arbitrary unimodal distribution of random parameters. The algorithm's features include the selection of a confidence set bounded by the probability density surface of the random variable. To construct this set, the Monte Carlo method is used to generate and label a random sample in combination with a support vector machine (SVM).</p></jats:p>