Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

Abstract

Economic development, variation in weather patterns and natural disasters focus attention on the management of water resources. This paper reviews the literature on the development of mathematical programming models for water resource management under uncertainty between 2010 and 2017. A systematic search of the academic literature identified 448 journal articles on water resource management for examination. Bibliometric analysis is employed to investigate the methods that researchers are currently using to address this problem and to identify recent trends in research in the area. The research reveals that stochastic dynamic programming and multistage stochastic programming are the methods most commonly applied. Water resource allocation, climate change, water quality and agricultural irrigation are amongst the most frequently discussed topics in the literature. A more detailed examination of the literature on each of these topics is included. The findings suggest that there is a need for mathematical programming models of large-scale water systems that deal with uncertainty and multiobjectives in an effective and computationally efficient way.

Multi-Criteria Decision-Making Methods to Address Water Allocation Problems: A Systematic Review

“…Overall, this review research study reveals that NSGA II was the most commonly applied method, and GA and LP follow. In contrast to our conclusion, Archibald and Marshall [6] in their review study reported that stochastic dynamic programming and multistage stochastic programming were the frequently used methods. However, their review was concentrated on the broad aspect of water resource management and the review time-limited between 2010 and 2017.…”

“…They indicated more publications were released after 2011 and there were equal to or less than one per year until 2004. Our results also reflect on those of Archibald and Marshall [6], who reviewed the application of mathematical programming on water resources management. They found that the number of publications increased from January 2010 to December 2017.…”

“…China has the first position; almost half of the publications originate from there. Similar review results were obtained by Archibald and Marshall [6] and Bhateria and Jain [101], which proved China is the top-ranked country. This may be due to the presence of multiple waterways and transboundary rivers that require the application of multi-objective decision-making tools.…”

Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs

“…The results obtained in terms of the number of publications per year are also shown in Table 1, from 2009 to 2019. These findings were in concordance with the ones found by [20], who performed a review of mathematical programming applications in water resource management under uncertainty. Based on this review, it is worth highlighting the growing importance of developing pricing strategies to improve the water management in water irrigation networks.…”

Water Sources Diagram and Its Applications

“…However, the complexity of many processes with respect to the presence of multiple contaminants in the equipment streams has led to the development of complex models and methods, many of them based on mathematical programming [2]. Rigorous models require a deep knowledge of the process, which is different for each type of industry.…”