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Preprints, Working Papers, ... Year : 2023

Decomposition Methods for Monotone Two-Time-Scale Stochastic Optimization Problems

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.
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Dates and versions

hal-02013969 , version 1 (11-02-2019)
hal-02013969 , version 2 (29-08-2023)

Identifiers

  • HAL Id : hal-02013969 , version 2

Cite

Tristan Rigaut, Pierre Carpentier, Jean-Philippe Chancelier, Michel de Lara. Decomposition Methods for Monotone Two-Time-Scale Stochastic Optimization Problems. 2023. ⟨hal-02013969v2⟩
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