Journal ArticleDOI
Scenarios for Multistage Stochastic Programs
TLDR
The case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model when no assumptions on convexity with respect to the random parameters are required is discussed.Abstract:
A major issue in any application of multistage stochastic programming is the representation of the underlying random data process. We discuss the case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model. No assumptions on convexity with respect to the random parameters are required. We emphasize the notion of representative scenarios (or a representative scenario tree) relative to the problem being modeled.read more
Citations
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Journal ArticleDOI
Scenario Reduction Algorithms in Stochastic Programming
Holger Heitsch,Werner Römisch +1 more
TL;DR: Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately for convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P.
Journal ArticleDOI
Scenario Reduction in Stochastic Programming
TL;DR: Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics in a convex stochastic programming problem with a discrete initial probability distribution.
Proceedings ArticleDOI
Scenario reduction and scenario tree construction for power management problems
TL;DR: Numerical experience is reported for constructing scenario trees for the load and spot market prices entering a stochastic portfolio management model of a German utility.
Journal ArticleDOI
The Design of Robust Value-Creating Supply Chain Networks: A Critical Review †
TL;DR: This paper argues for the assessment of SCN robustness as a necessary condition to ensure sustainable value creation and contributes to framing the foundations for a robust SCN design methodology.
Journal ArticleDOI
Scenario reduction in stochastic programming: An approach using probability metrics
TL;DR: Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics and efficient algorithms are developed that determine optimal reduced measures approximately.
References
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Journal ArticleDOI
Portfolio Selection: Efficient Diversification of Investments
Alan Stuart,Harry M. Markowitz +1 more
TL;DR: In this article, the authors defined asset classes technology sector stocks will diminish as the construction of the portfolio, and the construction diversification among the, same level of assets, which is right for instance among the assets.
Journal ArticleDOI
Scenarios and policy aggregation in optimization under uncertainty
TL;DR: This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Journal ArticleDOI
Generating Scenario Trees for Multistage Decision Problems
Kjetil Høyland,Stein W. Wallace +1 more
TL;DR: This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties, and argues that what are the relevant properties, will be problem dependent.
Journal ArticleDOI
Monte Carlo bounding techniques for determining solution quality in stochastic programs
TL;DR: It is shown that, in expectation, z^*"n is a lower bound on z* and that this bound monotonically improves as n increases, and confidence intervals are constructed on the optimality gap for any candidate solution x@^ to SP.