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Avtomatika i Telemekhanika, 2014, Issue 1, Pages 130–144
(Mi at6181)
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This article is cited in 12 scientific papers (total in 12 papers)
Stochastic Systems, Queuing Systems
Bilevel stochastic linear programming problems with quantile criterion
S. V. Ivanov Moscow Aviation Institute, Moscow, Russia
Abstract:
We propose a setting for a bilevel stochastic linear programming problem with quantile criterion. We study continuity properties of the criterial function and prove the existence theorem for a solution. We propose a deterministic equivalent of the problem for the case of a scalar random parameter. We show an equivalent problem in the form of a two-stage stochastic programming problem with equilibrium constraints and quantile criterion. For the case of a discrete distribution of random parameters, the problem reduces to a mixed linear programming problem. We show results of numerical experiments.
Citation:
S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Avtomat. i Telemekh., 2014, no. 1, 130–144; Autom. Remote Control, 75:1 (2014), 107–118
Linking options:
https://www.mathnet.ru/eng/at6181 https://www.mathnet.ru/eng/at/y2014/i1/p130
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Statistics & downloads: |
Abstract page: | 515 | Full-text PDF : | 120 | References: | 56 | First page: | 42 |
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