Implicit Mean-Variance Approach for Optimal Management of a Water Supply System under Uncertainty
Publication: Journal of Water Resources Planning and Management
Volume 139, Issue 6
Abstract
This study addresses the management of a water supply system under uncertainty. Water is taken from sources that include aquifers and desalination plants and conveyed through a distribution system to consumers under constraints of quantity and quality. The replenishment into the aquifers is stochastic, whereas the desalination plants can produce a large and reliable amount, but at a higher cost. The cost is stochastic because it depends on the realization of the replenishment into the aquifer. A new implicit mean-variance approach is developed and applied. It utilizes the advantages of implicit stochastic programming to formulate a small size and easy to solve convex external optimization problem (quadratic objective and linear constraints) that generates the mean-variance tradeoff without the need to solve a large-scale problem. The results are presented as a tradeoff between the expected value versus the standard deviation. At one end of the tradeoff curve, dependence on the aquifer results in low expected cost and higher cost variability. At the other end, when all of the water is taken from desalination, the cost is high with no variability (deterministic).
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Published In
Journal of Water Resources Planning and Management
Volume 139 • Issue 6 • November 2013
Pages: 634 - 643
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Nov 21, 2011
Accepted: Aug 31, 2012
Published online: Sep 4, 2012
Discussion open until: Feb 4, 2013
Published in print: Nov 1, 2013
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