A New Interval Two-stage Stochastic Programming with CVaR for Water Resources Management
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A New Interval Two-stage Stochastic Programming with CVaR for Water Resources Management Min Zhang1,2
· Kaiyan Xi1,2
Received: 4 December 2019 / Accepted: 21 July 2020 / © Springer Nature B.V. 2020
Abstract In area of water resources management, decision-makers usually need to make plans under various uncertainties in order to achieve the maximal total net benefits and prevent possible losses under risks arising from the indeterminacy. In this paper, we have incorporated the conditional value-at-risk, which has been widely used in portfolio selection problems for effective risk management, in the interval two-stage stochastic programming framework to perform trade-offs between economic objectives and associated risks. Moreover, based on the late progresses in Grey linear system, we have developed a new method to obtain a solution of the proposed model. In particular, this new approach can provide a number of decision alternatives under different coefficients, which help decision-makers make proper water supply plans according to their personal preferences. Finally, numerical experiments have been presented to demonstrate the validity and applicability of the proposed model for maintaining balance between profits and risks, as well as the efficiency of the new method for dealing with such model. Keywords Interval two-stage stochastic programming · CVaR · Water resources management · Grey linear programming
1 Introduction Water resources management problems are surrounded by a variety of uncertainties, including the randomness of the future available water amount and the indeterminacy of the economic data. To cope with uncertainties in both aspects, Huang and Loucks (2000) first developed the interval two-stage stochastic programming (ITSP), which is essentially a hybrid of two-stage stochastic programming and inexact optimization (grey system), to handle issues of resources allocation among multiple users. In recent years, ITSP has been widely applied in water resources management problems, such as water-resources allocation Min Zhang
[email protected] 1
State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi, 830011, China
2
University of Chinese Academy of Sciences, Beijing, 100049, China
M. Zhang, K. Xi
for various sectors (Huang et al. 2012; Khosrojerdi et al. 2019; Li et al. 2019), agricultural irrigation planning (Li et al. 2010; Zhang et al. 2018) and water quality management (Huang 1996; Zhang and Li 2014; Martinsen et al. 2019). In the mathematical model of ITSP, the expectation, as a risk-neutral measure, is used to evaluate the future profits in a two-stage stochastic programming. As it is known, the expectation performs well in situations where the interest lies in long-range operation and where stochastic ups and downs can safely average out (Rockafellar and Uryasev 2013). However, the water resources management has a distinct short-run focus and it may suffer from serious risks under extreme circumstances, s
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