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

The paper is devoted to the stochastic optimistic bilevel optimization problem with quantile criterion in the upper level problem. If the probability distribution is finite, the problem can be transformed into a mixed-integer nonlinear optimization problem. We formulate assumptions guaranteeing that an optimal solution exists. A production planning problem is used to illustrate usefulness of the model. Copyright © 2017 John Wiley & Sons, Ltd.