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

Abstract

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.

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

“…A chance constraint programming model includes groups of constraints, which do not need to be satisfied in all possible future scenarios. Decision-makers specify the probabilities with which constraints are satisfied individually [74,75,108,110,135,171,172,203,234] or jointly [72,73,119,137,228,231,244]. Closely related to this approach, Dong et al [44] propose a stochastic programming model with two objectives: maximising system benefits and maximising the probability that the constraints are satisfied.…”

Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

“…Guan and Philpott (2011) applied the multi‐stage approach to a production planning problem for Fonterra, a leading company in the New Zealand dairy industry, taking into account uncertain milk supply, price–demand curves, and contracting. Other applications of MSSP include water management for farm irrigation (Zhang et al., 2017b, 2019; Li and Hu, 2020). More generally, some of applications of multi‐period planning are Kazemi Zanjani et al.…”

A multi-stage stochastic integer programming approach for locating electric vehicle charging stations

“…in [12] and [42]. Moreover, in view of the numerical difficulties encountered when solving large-size instances, solution algorithms based on metaheuritics, and in particular on genetic algorithms, have also been proposed to tackle multi-stage stochastic optimization problems arising in various application domains such as financial portfolio optimization (Chan et al [3], Yang [51], Zhang et al [54]), industrial maintenance planning (Yahyatabar and Najafi [50]) or water resource management ( [56]).…”

“…[3], [51], [54]), [50] and [56], we propose a genetic algorithm (GA) to find good quality solutions when optimal solutions are difficult to obtain. Note that our GA is based on a fine analysis of the specific features of our problem and seeks to exploit them as best as possible at several critical steps of the algorithm, namely the building of an initial population, the evaluation of the fitness function of each individual and the definition of the crossover and mutation operators.…”