Implicit mean-variance approach for optimal management of a water supply system under uncertainty

Mashor Housh, Avi Ostfeld, Uri Shamir

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Pages (from-to)634-643
Number of pages10
JournalJournal of Water Resources Planning and Management - ASCE
Issue number6
StatePublished - 2013
Externally publishedYes


  • Implicit mean-variance
  • Management
  • Optimal
  • Uncertainty
  • Water supply

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geography, Planning and Development
  • Water Science and Technology
  • Management, Monitoring, Policy and Law


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