We study multistage stochastic optimization problems using sample average approximation (SAA) and model predictive control (MPC) as solution approaches. MPC is frequently employed when the size of the problem renders stochastic dynamic programming intractable, but it is unclear how this choice affects out-of-sample performance. To compare SAA and MPC out-of-sample, we formulate and solve an inventory control problem that is driven by random prices. Analytic and numerical examples are used to show that MPC can outperform SAA in expectation when the underlying price distribution is right-skewed. We also show that MPC is equivalent to a distributional robustification of the SAA problem with a first-moment based ambiguity set.
Keehan D. S. T., Philpott A. B., Anderson E. J., (May 2023) Sample average approximation and model predictive control for inventory optimization. Preprint.