Decomposition methods for monotone two-time-scale stochastic optimization problems

Tristan Rigaut (), Pierre Carpentier (), Jean-Philippe Chancelier () and Michel Lara ()
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Tristan Rigaut: Schneider Electric
Pierre Carpentier: ENSTA Paris
Jean-Philippe Chancelier: École des Ponts ParisTech
Michel Lara: École des Ponts ParisTech

Computational Management Science, 2024, vol. 21, issue 1, No 28, 37 pages

Abstract: Abstract It is common that strategic investment decisions are made at a slow time-scale, whereas operational decisions are made at a fast time-scale. Hence, the total number of decision stages may be huge. In this paper, we consider multistage stochastic optimization problems with two time-scales, and we propose a time block decomposition scheme to address them numerically. More precisely, (i) we write recursive Bellman-like equations at the slow time-scale and (ii), under a suitable monotonicity assumption, we propose computable upper and lower bounds—relying respectively on primal and dual decomposition—for the corresponding slow time-scale Bellman functions. With these functions, we are able to design policies. We assess the methods tractability and validate their efficiency by solving a battery management problem where the fast time-scale operational decisions have an impact on the storage current capacity, hence on the strategic decisions to renew the battery at the slow time-scale.

Keywords: Dynamic programming; Decomposition methods; Long-term battery management; Multi-horizon; Two-time-scale (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-024-00510-5

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