The interval copula-measure Me based multi-objective multi-stage stochastic chance-constrained programming for seasonal
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ORIGINAL PAPER
The interval copula-measure Me based multi-objective multi-stage stochastic chance-constrained programming for seasonal water resources allocation under uncertainty Youzhi Wang1 • Ping Guo1,2 Received: 6 August 2020 / Revised: 7 October 2020 / Accepted: 16 October 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A copula-measure Me based interval multi-objective multi-stage stochastic chance-constrained programming (CMIMOMSP) model is proposed for water consumption optimization. It can conduct water allocation amid multiple users and multiple stages, and deal with the uncertainties presented as interval numbers, random fuzzy interval numbers, and stochastic variables. It improves upon multi-stage stochastic chance-constrained programming by introducing the multiobjective programming, and it can tradeoff the relationships amid economic benefit, full usage of water resources, and economic loss. It enhances the accuracy of copula function and conditional distribution function through proposing the interval functions. Besides, it can deal with the impact of the decision attitudes of managers on water allocation by formulating the function equation between water demand and the optimistic-pessimistic factor. The CMIMOMSP model is applied to a case study of the Heihe River Basin to verify its application. The results indicate that: (1) the optimisticpessimistic factors have different degrees of positive influences on water allocation for industrial, domestic and ecological sectors; (2) the joint violated probability and optimistic-pessimistic factor have various range of impacts on agricultural water allocation; (3) tthe objective function values have different variation tendencies with the rise of joint violated probabilities and optimistic-pessimistic factors. Its robustness is enhanced by comparing it with the three single-objective programming models. The CMIMOMSP model can provide various water allocation schemes for managers with different risk attitudes in semi-arid and arid districts. Keywords Interval copula function Interval conditional distribution Multi-objective programming Multi-stage stochastic programming Measure Me Uncertainty
1 Introduction Water resources play an important role in social and economic development, especially for arid and semi-arid regions. In recent years, the contradictions between water supplies and water demands become serious, and water resources competitions amid multiple water users
& Ping Guo [email protected] 1
Center for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China
2
Wuwei ExperiMental Station for Efficient Water Use in Agriculture, Ministry of Agriculture and Rural Affairs, Wuwei 733000, China
aggravate with variations of climate change and human activities (Gu et al. 2013; Zeng et al. 2014; Zhang et al. 2017, 2019). Besides, seasonal uneven distributions of water resources increase the difficulties of water management. Therefore, it is essential to optimize water resources am
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