Stochastic linear programming and Conditional Value at Risk for water resources management

Roger Brian Webby, John Boland, Phil Howlett, Andrew Metcalfe


A mathematical analysis is presented for decision support for managing water resources in a water-limited environment. The water sources include rainfall, either direct or that held in reservoirs, shallow aquifers, river water withdrawal entitlements, and recycled water. Water from each source has its own characteristics of quality and thus suitability for use, quantity, temporal availability, environmental impact of use and cost to access. Water availability is modelled by a multivariate probability distribution. Relative values for salinity levels and nutrient or mineral loads are given and other water characteristics are summarised by a price for water from each source. We formulate and solve a stochastic linear program to find the optimal blend of the available sources while meeting quality and supply constraints. We apply these techniques to a common water resource management problem facing an Australian farmer, that of growing a summer crop usually reliant on irrigation. We compare alternate cropping decisions based on their risk of failing to meet supply or quality standards. Our measure of risk is Conditional Value-at-Risk.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.