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Scenario generation with distribution functions and correlations

Michal Kaut, Arnt-Gunnar Lium (2014)

Kybernetika

In this paper, we present a method for generating scenarios for two-stage stochastic programs, using multivariate distributions specified by their marginal distributions and the correlation matrix. The margins are described by their cumulative distribution functions and we allow each margin to be of different type. We demonstrate the method on a model from stochastic service network design and show that it improves the stability of the scenario-generation process, compared to both sampling and a...

Selected multicriteria shortest path problems: an analysis of complexity, models and adaptation of standard algorithms

Zbigniew Tarapata (2007)

International Journal of Applied Mathematics and Computer Science

The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness...

Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance

Vlasta Kaňková (2017)

Kybernetika

Economic and financial processes are mostly simultaneously influenced by a random factor and a decision parameter. While the random factor can be hardly influenced, the decision parameter can be usually determined by a deterministic optimization problem depending on a corresponding probability measure. However, in applications the “underlying” probability measure is often a little different, replaced by empirical one determined on the base of data or even (for numerical reason) replaced by simpler...

Stability of stochastic optimization problems - nonmeasurable case

Petr Lachout (2008)

Kybernetika

This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, ε -optimal solutions are considered. The setup is illustrated on consistency of a ε - M -estimator in linear regression model.

Stochastic bottleneck transportation problem with flexible supply and demand quantity

Yue Ge, Hiroaki Ishii (2011)

Kybernetika

We consider the following bottleneck transportation problem with both random and fuzzy factors. There exist m supply points with flexible supply quantity and n demand points with flexible demand quantity. For each supply-demand point pair, the transportation time is an independent positive random variable according to a normal distribution. Satisfaction degrees about the supply and demand quantity are attached to each supply and each demand point, respectively. They are denoted by membership functions...

Stochastic dynamic programming with random disturbances

Regina Hildenbrandt (2003)

Discussiones Mathematicae Probability and Statistics

Several peculiarities of stochastic dynamic programming problems where random vectors are observed before the decision ismade at each stage are discussed in the first part of this paper. Surrogate problems are given for such problems with distance properties (for instance, transportation problems) in the second part.

Stochastic geometric programming with an application

Jitka Dupačová (2010)

Kybernetika

In applications of geometric programming, some coefficients and/or exponents may not be precisely known. Stochastic geometric programming can be used to deal with such situations. In this paper, we shall indicate which stochastic programming approaches and which structural and distributional assumptions do not destroy the favorable structure of geometric programs. The already recognized possibilities are extended for a tracking model and stochastic sensitivity analysis is presented in the context...

Stochastic goal programming wth recourse

Antonio Heras Martínez, Ana García Aguado (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

In this article we discuss several alternative formulations for Stochastic Goal Programming. Only one of these models, which is a particular case of the Stochastic Programs with Recourse, is also compatible with Bayesian Decision Theory. Moreover, it is posible to approximate its solutions by means of an iterative algorithm.

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

Vlasta Kaňková, Vadim Omelčenko (2018)

Kybernetika

Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem 𝒰 of the utility functions. Especially, considering 𝒰 : = 𝒰 1 (where 𝒰 1 is a system of non decreasing concave nonnegative utility functions) we obtain...

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