# Debora Mahlke's A Scenario Tree-Based Decomposition for Solving Multistage PDF

By Debora Mahlke

ISBN-10: 3834814091

ISBN-13: 9783834814098

Optimization difficulties related to doubtful info come up in lots of components of commercial and financial functions. Stochastic programming offers an invaluable framework for modeling and fixing optimization difficulties for which a likelihood distribution of the unknown parameters is on the market. stimulated by way of functional optimization difficulties happening in strength structures with regenerative strength offer, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer versions. for his or her answer, the writer proposes a singular decomposition strategy which will depend on the concept that of splitting the underlying state of affairs tree into subtrees. in line with the formulated types from power creation, the set of rules is computationally investigated and the numerical effects are mentioned.

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**Extra info for A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs**

**Sample text**

A further technical parameter is the maximum power gradient Δmax i describing by how much the production level can be increased within one time period. In order to avoid increased thermal stress of a power plant, the parameters θiup and θidown are used denoting the minimum running and the minimum down time, respectively. This means that once a plant starts to operate, it has to keep on running for at least θiup time periods. Analogously, the plant must remain oﬀ for at least θidown time periods, once it is turned oﬀ.

Here, the eﬃciency is associated with the ratio of the consumed power and the produced power pit . Concerning a charging unit k ∈ Kj of storage j ∈ J , the function ηjin (sin kt ) is introduced, reﬂecting the ratio between the consumed electric power sin kt and the converted power to be stored. , having the same eﬃciency function ηjin . 1: Eﬃciency of a power plant 22 Chapter 3. Mathematical Modeling the ratio of the power removed from the storage to the discharged power ext out sout lt . Finally, the function ηj (slt ) describes the eﬃciency corresponding to the ratio of discharged power sout lt and power procured from outside.

2 The S-OPGen Model With the notation described above, we can formulate a multistage stochastic model for our problem. The variables are no longer only assigned to a time step t ∈ T , but also depend on the scenarios of the stochastic process ξ represented by the scenario tree Γ = (N , A). If we use the nonanticipativity condition requiring that a decision in period t may only depend on 36 Chapter 3. Mathematical Modeling realizations of the stochastic data up to t, the variables can carry the node index n ∈ N , instead of index t ∈ T and s ∈ S.

### A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs by Debora Mahlke

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