Bounds in multi-horizon stochastic programs

Maggioni, Francesca; Allevi, Elisabetta; Tomasgård, Asgeir

doi:10.1007/s10479-019-03244-9

Cited by 13 publications

(10 citation statements)

References 30 publications

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“…The multiscale structure could then simply mean that uncertainty is lost within a given stage (cf., e.g., Moriggia et al 2018). More advanced approaches do consider some uncertainty [e.g., the so-called multihorizon approach originally suggested in Kaut et al (2014) and subsequently studied and applied in Seljom and Tomasgard (2017), Skar et al (2016), Werner et al (2013), Zhonghua et al (2015), Maggioni et al (2019)], but the resulting paths do not necessarily connect with subsequent elements in the scenario tree/lattice. Hence, the multi-horizon approach is not appropriate for the present problem, as the key requirement of two time scales which may be assumed to run completely independent from each other, is not given.…”

Section: Introductionmentioning

confidence: 99%

Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Ackooij¹,

Escobar

Glanzer

et al. 2019

Comput Manag Sci

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The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. However, also this approach has its limitations, since quite often the models for costs and revenues are subject to model error. Under a prudent valuation, the possible model error should be incorporated into the calculation. In this paper, we consider the valuation of a power plant under ambiguity of probability models for costs and revenues. The valuation is done by stochastic dynamic programming and on top of it, we use a dynamic ambiguity model for obtaining the prudent minimax valuation. For the valuation of the power plant under model ambiguity we introduce a distance based on the Wasserstein distance. Another highlight of this paper is the multiscale approach, since decision stages are defined on a weekly basis, while the random costs and revenues appear on a much finer scale. The idea of bridging stochastic processes is used to link the weekly decision scale with the finer simulation scale. The applicability of the introduced concepts is broad and not limited to the motivating valuation problem.

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Section: Introductionmentioning

confidence: 99%

Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Ackooij¹,

Escobar

Glanzer

et al. 2019

Comput Manag Sci

View full text Add to dashboard Cite

show abstract

“…A linear interpolation would simply not be in line with the essence of the problem that one does not know in advance if/when one will run out of stock during the week. • Multi-horizon stochastic programming A solution approach for a class of problems which are of a similar flavour, yet crucially different in nature, is called multi-horizon stochastic programming (see [21,27,41,42,46,48]). Infrastructure planning problems, being the original motivation by Kaut et al [21], typically involve (rarely happening) strategic decisions as well as operational tasks (daily business).…”

Section: Comparison With Other Modeling Approachesmentioning

confidence: 99%

Multiscale stochastic optimization: modeling aspects and scenario generation

Glanzer

Pflug

2019

Comput Optim Appl

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Real-world multistage stochastic optimization problems are often characterized by the fact that the decision maker may take actions only at specific points in time, even if relevant data can be observed much more frequently. In such a case there are not only multiple decision stages present but also several observation periods between consecutive decisions, where profits/costs occur contingent on the stochastic evolution of some uncertainty factors. We refer to such multistage decision problems with encapsulated multiperiod random costs, as multiscale stochastic optimization problems. In this article, we present a tailor-made modeling framework for such problems, which allows for a computational solution. We first establish new results related to the generation of scenario lattices and then incorporate the multiscale feature by leveraging the theory of stochastic bridge processes. All necessary ingredients to our proposed modeling framework are elaborated explicitly for various popular examples, including both diffusion and jump models. Keywords Stochastic programming • Scenario generation • Bridge process • Stochastic bridge • Diffusion bridge • Lévy bridge • Compound Poisson bridge • Simulation of stochastic bridge • Multiple time scales • Multi-horizon • Multistage stochastic optimization

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“…MHSP was further formalised in Escudero & Monge (2018). In addition, the bounds and formulation of MHSP have been studied (Maggioni et al, 2020). The literature on MHSP is much more sparse compared with multi-stage stochastic programming.…”

Section: Introductionmentioning

confidence: 99%

Decomposition methods for multi-horizon stochastic programming

Zhang,

Grossmann,

Tomasgard

2024

Preprint

Self Cite

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Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the block separable structure of multi-horizon stochastic linear programming, and establish that it can be decomposed by Benders decomposition and Lagrangean decomposition. In addition, we propose parallel Lagrangean decomposition with primal reduction that, (1) solves the scenario subproblems in parallel, (2) reduces the primal problem by keeping one copy for each scenario group at each stage, and (3) solves the reduced primal problem in parallel. We apply the parallel Lagrangean decomposition with primal reduction, Lagrangean decomposition and Benders decomposition to solve a stochastic energy system investment planning problem. The computational results show that: (a) the Lagrangean type decomposition algorithms have better convergence at the first iterations to Benders decomposition, and (b) parallel Lagrangean decomposition with primal reduction is very efficient for solving multi-horizon stochastic programming problems. Based on the computational results, the choice of algorithms for multi-horizon stochastic programming is discussed.

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Bounds in multi-horizon stochastic programs

Cited by 13 publications

References 30 publications

Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

Multiscale stochastic optimization: modeling aspects and scenario generation

Decomposition methods for multi-horizon stochastic programming

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