Inexact stochastic dynamic programming method and application to water resources management in Shandong China under unce
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ORIGINAL PAPER
Inexact stochastic dynamic programming method and application to water resources management in Shandong China under uncertainty J. J. Gu • P. Guo • G. H. Huang
Published online: 8 November 2012 Ó Springer-Verlag Berlin Heidelberg 2012
Abstract In this study, an interval parameter multistage joint-probability programming (IMJP) approach has been developed to deal with water resources allocation under uncertainty. The IMJP can be used not only to deal with uncertainties in terms of joint-probability and intervals, but also to examine the risk of violating joint probabilistic constraints in the context of multistage. The proposed model can handle the economic expenditure caused by regional water shortage and flood control. The model can also reflect the related dynamic changes in the multi-stage cases and the system safety under uncertainty. The developed method is applied to a case study of water resources allocation in Shandong, China, under multistage, multireservoir and multi-industry. The violating reservoir constraints are addressed in terms of joint-probability.
J. J. Gu Institute of Ecological Simulation and Urban Ecology, Beijing Normal University, Beijing 100875, China P. Guo (&) Centre for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China e-mail: [email protected] P. Guo Environmental Science and Engineering Program, University of Northern British Columbia, Prince George, BC V2N 4Z9, Canada G. H. Huang Environmental Systems Engineering Program, University of Regina, Regina, Saskatchewan S4S 0A2, Canada G. H. Huang Energy and Environmental Research Center, North China Electric Power University, Beijing 102206, China
Different risk levels of constraint lead to different planning. The obtained results can help water resources managers to identify desired system designs under various economic, environment and system reliability scenarios. Keywords Dynamic Joint probability Multistage Scenarios Uncertainty Water resources List of symbols Variables Objective function, total benefits of the system f Auxiliary variable, distributary volume from Rtk1 reservoir 1 (Tianzhuang reservoir) under the scenario of K1 in period t Auxiliary variable, distributary volume from R tk1 k2 reservoir 2 (Bashan reservoir) in period t under the situation when scenario K1 and K2 are in joint probability form Auxiliary variable, storage water volume of S tk1 reservoir 1 (Tianzhuang reservoir) under the scenario of K1 in period t Auxiliary variable, storage water volume of Stk1 k2 reservoir 2 (Bashan reservoir) in period t under the situation when scenario K1 and K2 are in joint probability form Decision variable, the promised water supply to Xt county from the reservoir Decision variable, the promised water supply to Xit each industry from the reservoir SHtk1 k2 Decision variable, the gap of water shortage between the actual water supply and the promised water supply to three industries from the reservoir in period t in the situation when scenario K1 and K2
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