Water resources management under uncertainty: factorial multi-stage stochastic program with chance constraints

Abstract

Due to rapid growth of population and development of economy, water resources allocation problems have aroused wide concern. Therefore, optimization of water resources systems is complex and uncertain, which is a severe challenge faced by water managers. In this paper, a factorial multi-stage stochastic programming with chance constraints approach is developed to deal with the issues of water-resources allocation under uncertainty and risk as well as their interactions. It can deal with uncertainties described as both interval numbers and probability distributions, and can also support the risk assessment within a multistage context. The solutions associated with different risk levels of constraint violation can be obtained, which can help characterize the relationship between the economic objective and the system risk. The inherent interactions between factors at different levels and their effects on total net benefits can be revealed through the analysis of multi-parameter interactions.

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

“…Tables 2 and 3 present the information regarding seasonal flows under different probabilities. Tables 1-3 derive from [1]. In the case of insufficient water resources, the water for municipal sector should be delivered preferentially since the highest benefit will be brought when the municipal water demand is satisfied, while the highest penalty will be produced if the promised water is not delivered, followed by the industrial and agricultural sectors which correspond to lower benefits and penalties (see Table 4).…”

“…Models (1), (2), and (3) do not readily assess the risks, and they only deal with uncertainties in the right hand side such as the water flow . It is difficult to handle uncertainties in both the left and right hand sides (i.e., , NB , and ) [1] which are presented as interval with stochastic normal distributed boundaries. In view of the above considerations, Liu et al [1] combined chance constrained programming (CCP, initiated by Charnes and Cooper [15]) with IMSP to propose the following inexact multistage stochastic programming model with chance constraints to solve problems with the request that chance constraints should hold at least with prescribed levels of probability (i.e., confidence levels):…”

“…Due to unreasonable exploitation and utilization of water resources, water pollution, and extreme weather conditions, more and more countries and regions are faced with different degrees of water shortage. Making the best use of limited water resources premises the sustainable development of economy and society [1]. In the past few decades, many researchers have applied optimization techniques [2][3][4][5][6][7] to deal with uncertainties in a number of system components and their interrelationships within water resources systems [8].…”

“…In water resources management, using CCP is conducive to not only making decisions of water allocation but also gaining insights into the tradeoffs between economic objectives and some policy factors for a water resource manager [19]. For instance, Liu et al [1] provided a factorial multistage stochastic programming with chance constraints to deal with the issues of constraint-violation risks and interactive uncertainties in water resources management systems. However, this kind of CCP models can only be solved in some special cases.…”

Exploration of an Optimal Policy for Water Resources Management Including the Introduction of Advanced Sewage Treatment Technologies in Zaozhuang City, China

“…Lotze-Campen et al [15] presented a mathematical programming model that contained regional economic conditions and water constraints to study agricultural production and its environmental impacts. Liu et al [16] developed factorial multi-stage stochastic programming with a chance-constraints approach to analyze the relationship between economic objectives and water resources management system risk. Davijani et al [17] presented a two-objective socio-economic model for optimal water allocation among industry, agriculture, and municipal sectors.…”