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...

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Bibliographic Details
Published in:Applied stochastic models in business and industry Vol. 33; no. 5; pp. 544 - 554
Main Authors: Dempe, Stephan, Ivanov, Sergey, Naumov, Andrey
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.09.2017
Subjects:
bilevel optimization
mixed‐integer programming problem
Optimization
Production planning
quantile objective function
stochastic optimization
VaR‐criterion
ISSN:1524-1904, 1526-4025
Online Access:Get full text
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Summary: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.
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ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.2254