Table of Contents Author Guidelines Submit a Manuscript
Scientific Programming
Volume 2017 (2017), Article ID 1680813, 14 pages
Research Article

Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

1College of Water Conservancy and Hydropower, School of Science, Hebei University of Engineering, Handan 056038, China
2College of Arts, Hebei University of Engineering, Handan 056038, China
3School of Economics and Management, Handan University, Handan 056038, China

Correspondence should be addressed to Minghu Ha

Received 25 December 2016; Accepted 23 May 2017; Published 20 June 2017

Academic Editor: Fabrizio Riguzzi

Copyright © 2017 Hong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to formulate water allocation schemes under uncertainties in the water resources management systems, an inexact multistage stochastic chance constrained programming (IMSCCP) model is proposed. The model integrates stochastic chance constrained programming, multistage stochastic programming, and inexact stochastic programming within a general optimization framework to handle the uncertainties occurring in both constraints and objective. These uncertainties are expressed as probability distributions, interval with multiply distributed stochastic boundaries, dynamic features of the long-term water allocation plans, and so on. Compared with the existing inexact multistage stochastic programming, the IMSCCP can be used to assess more system risks and handle more complicated uncertainties in water resources management systems. The IMSCCP model is applied to a hypothetical case study of water resources management. In order to construct an approximate solution for the model, a hybrid algorithm, which incorporates stochastic simulation, back propagation neural network, and genetic algorithm, is proposed. The results show that the optimal value represents the maximal net system benefit achieved with a given confidence level under chance constraints, and the solutions provide optimal water allocation schemes to multiple users over a multiperiod planning horizon.