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Download A Scenario Tree-Based Decomposition for Solving Multistage by Debora Mahlke PDF

By Debora Mahlke

ISBN-10: 3834814091

ISBN-13: 9783834814098

Optimization difficulties concerning doubtful info come up in lots of parts of commercial and fiscal purposes. Stochastic programming presents an invaluable framework for modeling and fixing optimization difficulties for which a likelihood distribution of the unknown parameters is obtainable. encouraged through sensible optimization difficulties happening in power platforms with regenerative power offer, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer types. for his or her answer, the writer proposes a singular decomposition strategy which is determined by the concept that of splitting the underlying situation tree into subtrees. according to the formulated versions from strength construction, the set of rules is computationally investigated and the numerical effects are mentioned.

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Additional resources for A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs

Example text

S}, F be the power set of Ω and finally let P({ω}) = ps with s ∈ S. e. the information observable until period t ∈ T . As ξ1 is deterministic, we have F1 = {∅, Ω} and assuming to have full information at the end of the planning horizon we require FT = F. By ξts we denote the value of the data scenario s at time t with s ∈ S and t ∈ T . Here, a scenario ξ s = (ξ1s , . . , ξTs ) corresponds to a realization of the process over the complete planning horizon T . , they are combined to a path. Hence, this tree is called scenario tree.

3. Polyhedral Investigations where Γs is the scenario tree induced by the nodes {v1 , . . , vT }, which are associated with scenario s. 5) refer to the restricted index set Ns := {v1 , . . , vT }. 6). Indeed, the deterministic switching polytope it is a special case of the stochastic switching polytope, where the scenario tree consists of a single path. 10) n ≥ 0, n for all n ∈ N \{1} and by T T xup vk − −xvT + k=i for i = 2, . . 11) xdown vk ≤ 1, for i = 2, . . , T − l + 1. 12) T xup vk + k=i+l ≤ 0, k=i+L T xvT − xdown vk k=i for all s ∈ S with corresponding path (v1 , .

Summarizing, none of the presented publications completely covers the problem we are focusing on. , uncertainty about wind power or regenerative energy supply in general is neglected. Further on, either the combinatorial aspects or the nonlinearities regarding the efficiency of the plants are not taken into account. To the best of our knowledge, no contributions of current literature consider a model which combines uncertainty, switching processes and partial load efficiency with a detailed description of the technical characteristics of the units, as done in this thesis.

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

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