On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

“…By [19], the problem (26) is equivalent to (21). Thus, combining the conclusions written previously, we formulate the following assertion.…”

“…The method applied in this paper is suggested in [19] for the reduction of the stochastic programming problem with a discrete distribution and the quantile criterion to a mixed integer linear programming problem, which can be solved by standard methods (for example, by the software package OPTI Toolbox for MATLAB). Note that for a fixed k , the problem (26) is a linear programming problem.…”

Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem

“…In the following theorem, it is shown that the optimization problems (4) and (15)- (20) are equivalent in the following sense [17]:…”

“…In , a method to reduce single‐stage stochastic programming problems to mixed‐integer optimization problems is considered for the case of a discrete distribution of the random parameters. In , this method is applied to two‐stage stochastic programming problems.…”

Moment Generating Function, Expectation and Variance of Ubiquitous Distributions with Applications in Decision Sciences: A Review

“…The distribution functions have been widely used in many disciplines. Readers may read Bakouch et al (2014), Hajmohammadi et al (2013), Jazi et al (2010), Kibzun et al (2013), Paisley et al (2012), Cowpertwait (2010), Griggs et al (2012), Ranodolph et al (2012), Stickel et al (2012), Zhang et al (2015), and Zhao et al (2017). Therefore, it is important to have a paper presenting the detail about distribution functions and their moment generating function, expectation, and variance.…”