An empirical analysis of scenario generation methods for stochastic optimization

• An empirical analysis of scenario generation methods is presented.
• Quasi-Monte Carlo, moment matching, and optimal quantization are compared.
• A new method called Voronoi cell sampling is proposed.
• The newsvendor model with and without risk measure is used for comparison.
• Voronoi cell sampling yields the lowest sample average approximation errors.

This work presents an empirical analysis of popular scenario generation methods for stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based on probability metrics, as well as a new method referred to as Voronoi cell sampling. Solution quality is assessed by measuring the error that arises from using scenarios to solve a multi-dimensional newsvendor problem, for which analytical solutions are available. In addition to the expected value, the work also studies scenario quality when minimizing the expected shortfall using the conditional value-at-risk. To quickly solve problems with millions of random parameters, a reformulation of the risk-averse newsvendor problem is proposed which can be solved via Benders decomposition. The empirical analysis identifies Voronoi cell sampling as the method that provides the lowest errors, with particularly good results for heavy-tailed distributions. A controversial finding concerns evidence for the ineffectiveness of widely used methods based on minimizing probability metrics under high-dimensional randomness.