Risk Aversion Based Inexact Stochastic Dynamic Programming Approach for Water Resources Management Planning under Uncertainty

Abstract

In this study, a dual interval robust stochastic dynamic programming (DIRSDP) method is developed for planning water resources management systems under uncertainty. As an extension of the existing interval stochastic dynamic programming (ISDP) method, DIRSDP can deal with two-stage stochastic programming (TSP)-based planning problems associated with dynamic features, input uncertainties, and multistage concerns. Compared with other optimization methods dealing with uncertainties, the developed DIRSDP method has advantages in addressing uncertainties with complex presentations and reflecting decision makers’ risk-aversion attitudes within its optimization process. Parameters in the DIRSDP model can be represented as probability distributions as well as single and/or dual intervals. Decision makers’ risk-aversion attitudes can be reflected through restricting the deviation of the recourse costs to a tolerance level. Water-allocation plans can then be developed based on the analysis of tradeoffs between the system benefit and solution robustness. The developed method is applied to a case of water resources management planning. The solutions are reasonable, indicating applicability of the developed methodology.

Research on Bi-Level Objective Programming Model of Water Resources Uncertainty Based on Water Rights Trading—A Case Study of the Yehe Irrigation District in Hebei Province, China

“…Dynamic programming (DP) constitutes a methodology for tackling multi-stage decision-making challenges, emphasizing the sequential nature of decision-making across various stages [32][33][34], By dividing the stages, determining the states and transfer equations, complex problems are decomposed into multiple sub-problems and solved step-by-step to ensure optimal decision-making at each stage, thus obtaining the global optimal solution. The most crucial part of this approach is the state transition equation, which reflects the transition pattern from stage j − 1 to stage j.…”

Dynamic Programming Approach in Aggregate Production Planning Model under Uncertainty

“…Dynamic Programming is a strong formal instrument that may be utilized for the purpose of addressing a wide variety of multi-stage decision-making issues [32]. Since its origin in the middle of the 1950s by Bellman 1957, DP has developed into a common tool in a variety of fields [26], including but not limited to operations research, systems analysis, engineering, data analysis, control, and computer science, amongst others [22], [2], [33]. The fact that one only needs to solve a little fraction of each subproblem in order to complete DP successfully is one of its strengths [34].…”

“…A form of intermediate production planning known as aggregate production planning, or APP, has a time horizon of three to eighteen months and is used to establish the optimum solution level of production, stockpiles, and personnel management for each planning period within the form of limited factors of production and other constraints [1], [2]. The preferred APP strategy is capacity.…”

Rural Sustainable Environmental Management

“…This approach can provide decision-makers with reliable and robust management suggestions that are "immune" to the uncertainty due to data perturbations. In addition, a risk aversion based inexact stochastic dynamic programming method for water resources planning under uncertainty [18], an optimal design of a distributed energy system based on the functional interval model allowing reduction of carbon emission [19], a price-forecast-based irrigation scheduling optimization model under the response of fruit quality and price to water [20], and a multi-objective hierarchical model for irrigation planning in the complex canal system [21], were studied. These new approaches can provide more reliable and scientific advice on planting, irrigation, and energy supply, which will be favorable for the sustainable development of agriculture.…”