Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem. (26th April 2017)

• Record Type: Journal Article
• Authors: Dempe, Stephan; Ivanov, Sergey; Naumov, Andrey
• Is Part Of: Applied stochastic models in business and industry. Volume 33:Number 5(2017)
• Page Start: 544
• Page End: 554
• Publication Date: 2017-04-26
• Subjects: bilevel optimization -- quantile objective function -- stochastic optimization -- VaR‐criterion -- mixed‐integer programming problem; Stochastic analysis -- Periodicals; Stochastic processes -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Industrial management -- Mathematical models -- Periodicals; 338.00151923
• DOI: 10.1002/asmb.2254
• Languages: English
• ISSNs: 1524-1904

Abstract

Abstract : 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.