A dam management problem with energy production as an optimal switching problem

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2023-12-29 DOI:10.1002/asmb.2840

Etienne Chevalier, Cristina Di Girolami, M'hamed Gaïgi, Elisa Giovannini, Simone Scotti

引用次数: 0

Abstract

We consider an optimal stochastic control problem for a dam. Electrical power production is operating under an uncertain setting for electricity market prices and water level which has to be kept under control. Indeed, the water level inside the basin cannot exceed a certain threshold for safety reasons, and at the same time cannot decrease below another threshold in order to keep power production active. We model this situation as a mixed control problem with regular and switching controls under constraints. We characterize the value function as solution of an HJB equation and provide some numerical approximating methods. We shall illustrate by numerical examples the main achievements of the present approach.

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以能源生产为最佳转换问题的大坝管理问题

我们考虑的是大坝的最优随机控制问题。电力生产是在电力市场价格和水位不确定的情况下进行的，而水位必须保持在可控范围内。实际上，为了安全起见，流域内的水位不能超过某个临界值，同时也不能低于另一个临界值，以保持电力生产的积极性。我们将这种情况建模为一个混合控制问题，其中包含约束条件下的常规控制和开关控制。我们将值函数表征为 HJB 方程的解，并提供了一些数值近似方法。我们将通过数值示例说明本方法的主要成果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.