2000
DOI: 10.1023/a:1019206915174
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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.

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Cited by 399 publications
(21 citation statements)
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“…Here, the scenario nodes are plotted according to the generated scenario values, except for the root node, which is set to 1 for simplicity. For each stock, we can see from Figure 3 that the generated scenario tree includes both optimistic and pessimistic scenarios at each stage, satisfying the property that a good scenario generator should possess [29]; meanwhile, the child nodes emanating from distinct ancestor nodes are generally different, which is consistent with the remarks made in Section 2.1. Appl.…”
Section: Numerical Experimentssupporting
confidence: 79%
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“…Here, the scenario nodes are plotted according to the generated scenario values, except for the root node, which is set to 1 for simplicity. For each stock, we can see from Figure 3 that the generated scenario tree includes both optimistic and pessimistic scenarios at each stage, satisfying the property that a good scenario generator should possess [29]; meanwhile, the child nodes emanating from distinct ancestor nodes are generally different, which is consistent with the remarks made in Section 2.1. Appl.…”
Section: Numerical Experimentssupporting
confidence: 79%
“…It should be noticed that the prerequisite of the scenario reduction technique is that a large scenario tree should be generated in advance as an input. As for more other methods for scenario generation, the readers are referred to the review papers [29,30].Most of scenario tree generation methods either need to generate a large number of scenarios or depend on sophisticated mathematical models. The simulation, estimation and solution process of the complicated mathematical model will be very time-consuming.…”
mentioning
confidence: 99%
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“…There are many methods for generating scenarios, see Dupačová et al (2000) for an overview. Some of these methods try to generate scenarios that match a given set of speci cations for their marginal distributions and the dependence between them, where the latter is almost always speci ed using the correlation (or variance-covariance) matrix.…”
Section: Introductionmentioning
confidence: 99%
“…The two-stage SLP can be expanded to a multi-stage problem. A finite number of the scenarios, corresponding to sequences of realizations of random variables at each stage, must be specified to apply the multi-stage SLP with recourse (Dupač ová et al 2000). The multi-stage SLP for reservoir operation seems to be a viable approach if we can identify stages at which a decision is required, and when release decisions taken at any stage of the decision process do not depend on future realizations of the inflows or on future release decisions.…”
Section: Introductionmentioning
confidence: 99%