On the two-stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters

Authors:
A. V. Naumov;I. M. Bobylev
Affiliations:
Moscow State Aviation Institute, Moscow, Russia;Moscow State Aviation Institute, Moscow, Russia
Venue:
Automation and Remote Control
Year:
2012

Citing 3
Cited 3

Solution to a two-step logistics problem in a quintile statement

Automation and Remote Control
A Stochastic Programming Approach to the Airline Crew Scheduling Problem

Transportation Science
Stochastic mathematical programs with equilibrium constraints

Operations Research Letters

On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

Automation and Remote Control
On approximate computation of the quantile criterion

Automation and Remote Control
Bilevel stochastic linear programming problems with quantile criterion

Automation and Remote Control

Quantified Score

Hi-index	0.00

Visualization

Abstract

Consideration was given to the two-stage problem of stochastic linear programming with a discrete distribution of the random parameter vector. The property of continuity of the quantile function in strategy was proved, the sufficient conditions for existence of solution were formulated, and an algorithm to determine the guaranteeing solution was constructed on the basis of the confidence method and the duality theorem. A deterministic equivalent of the considered problem in the form of a linear programming problem was given for the scalar case.