Numerical evaluation of approximation methods in stochastic programming

Abstract

We study an approach for the evaluation of approximation and solution methods for multistage linear stochastic programmes by measuring the performance of the obtained solutions on a set of out-of-sample scenarios. The main point of the approach is to restore the feasibility of solutions to an approximate problem along the out-of-sample scenarios. For this purpose, we consider and compare different feasibility and optimality based projection methods. With this at hand, we study the quality of solutions to different test models based on classical as well as recombining scenario trees.

Keywords:

• multistage stochastic programming
• scenario tree
• out-of-sample evaluation

AMS Subject Classifications:

• 90C15
• 90C39
• 90C59
• 49M25

Acknowledgements

We are grateful to Teemu Pennanen for motivating us to this work and to Prof. Werner Römisch for his help and encouragement. This work was supported by the Bundesministerium für Bildung und Forschung (BMBF) under the grant 03SF0312E, which is gratefully acknowledged.