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REDUCTION OF TWO-STAGE PROBABILISTIC OPTIMIZATION PROBLEMS WITH DISCRETE DISTRIBUTION OF RANDOM DATA TO MIXED INTEGER PROGRAMMING PROBLEMS

Vladimir Norkin(norkin***at***i.com.ua)
Andrey Kibzun(kibzun***at***mail.ru)
Andrey Naumov(naumovav***at***mail.ru)

Abstract: We consider models of two-stage stochastic programming with a quantile second stage criterion and optimization models with a chance constraint on the second stage objective function values. Such models allow to formalize requirements to reliability and safety of the system under consideration, and to optimize the system in extreme conditions. We suggest a method of equivalent transformation of such models under a discrete distribution of random parameters to mixed integer programming problems. The number of auxiliary Boolean variables in the latter problems equals to the number of possible scenarios for random data. The obtained mixed integer optimization problems are supposed to be solved by contemporary discrete optimization software. As an illustration, results of a numerical experiment with a small test problem are presented.

Keywords: Stochastic programming, two-stage problems, quantile programming, chance constraints, deterministic equivalent, mixed integer programming.

Category 1: Stochastic Programming

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: To appear in "Cybernetics and Systems Analysis", Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kiev, April 2013.

Download: [PDF]

Entry Submitted: 04/19/2013
Entry Accepted: 04/19/2013
Entry Last Modified: 04/19/2013

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