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

Abstract

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. References F. J. Vasko, D. D. Newhart, and A. D. Strauss. Coal blending models for optimum cokemaking and blast furnace operation. Journal of the Operational Research Society, 56: 235--243, 2005. doi:10.1057/palgrave.jors.2601846 R. T. Rockafellar, and S. Uryasev. Conditional Value-at-Risk for General Loss Distributions. Journal of Banking and Finance, 26: 1443--1471, 2002. doi:10.1016/S0378-4266(02)00271-6 G. Yamout, and M. El-Fadel. An optimisation approach for multi-sector water supply management in the Greater Beirut area. Water Resources Management, 19: 791--812, 2005. doi:10.1007/s11269-005-3280-6 J. Liu, C. Men, V. E. Cabrera, S. Uryasev, and C. W. Fraisse. CVaR model for optimizing crop insurance under climate variability. Research Report 2006-1, Risk Management and Financial Engineering Lab, University of Florida, 2006. http://www.ise.ufl.edu/uryasev/pubs.html