Assessing policy quality in multi-stage stochastic programming

Abstract

Solving a multi-stage stochastic program with a large number of scenarios and a moderate-to-large number of stages can be computationally challenging. We develop two Monte Carlo-based methods that exploit special structures to generate feasible policies. To establish the quality of a given policy, we employ a Monte Carlo-based lower bound (for minimization problems) and use it to construct a confidence interval on the policy's optimality gap. The confidence interval can be formed in a number of ways depending on how the expected solution value of the policy is estimated and combined with the lower-bound estimator. Computational results suggest that a confidence interval formed by a tree-based gap estimator may be an effective method for assessing policy quality. Variance reduction is achieved by using common random numbers in the gap estimator.