Monte Carlo techniques for estimating solution quality in stochastic groundwater management models

For computational purposes, a stochastic groundwater management model with minimizing value z* is often approximately solved by randomly sampling n realizations of the model's stochastic parameters, and then solving the resulting `approximating problem' for (x*_n, z*_n). It can be shown that, in expectation, z*_n is a lower bound on z* and that this lower bound monotonically improves as n increases. Using this result, an approach based on Monte Carlo sampling and solution of multiple instances of the n-scenario approximating problem is applied to construct confidence intervals on the optimality gap for any candidate solution x, such as x = x*_n. A sampling procedure based on common random numbers ensures non-negative estimates of the optimality gap and provides significant variance reduction over naive sampling on a test problem involving the location of pumping wells for contaminant plume containment.