Ghina Yamout, Kirk Hatfield, H. Edwin Romeijn
Comparison of new Conditional Value-at-Risk based risk management models for optimal allocation of uncertain water supplies
Five models are developed to examine water resource allocation when available supplies are uncertain: (1) a deterministic expected value model, (2) a
scenario analysis model, (3) a two-stage stochastic model with recourse, (4) a Conditional Value-at Risk (CVaR) objective function model, and (5) a CVaR
constraint model. The models are applied over a region of East-Central Florida previously defined as a water caution area. Results show the deterministic
expected value model underestimates system costs and water shortage. Furthermore, the expected value model produces identical cost estimates for different
standard deviations distributions of water supplies with identical mean. From the scenario analysis model, it is again demonstrated that the expected value
of results taken from many scenarios underestimates costs and water shortages. Using a two-stage stochastic mixed integer formulation with recourse permits
an improved representation of uncertainties and real-life decision-making which in turn predicts higher costs. The inclusion of CVaR objective function in
the two-stage stochastic mixed integer formulation with recourse provides for the optimization and control of high risk events. Minimizing CVaR does not,
however, permit control of lower risk events. Constraining CVaR while minimizing cost, on the other hand, allows for the control of high risk events while
minimizing the costs of all events. Results show CVaR exhibits continuous and consistent behavior with respect to the confidence level, when compared to
Value-at-Risk (VaR).