Journal
AUTOMATION AND REMOTE CONTROL
Volume 75, Issue 1, Pages 107-118Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0005117914010081
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Funding
- Russian Foundation for Basic Research [11-07-00315a, 12-07-13108-ofi-m-RZhD]
- Federal Goal-oriented Program Scientific and Educational Personnel of Innovative Russia [1.2.2, 14.740.11.1128]
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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.
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