Robust and stochastic multistage optimisation under Markovian uncertainty with applications to production/inventory problems

A generic class of multistage optimisation problems related to production/inventory management under Markovian uncertainty is introduced and investigated. For each instance in the class, it is shown how to construct state-space representable uncertainty sets at any probability level, thus leading to efficient resolution of both the stochastic and robust versions of the problem. Computational experiments aimed at comparing the optimal strategies corresponding to both versions in terms of risk are then reported and discussed; it is observed that the robust optimisation approach can significantly outperform the stochastic optimisation approach when targeting lower risk levels (typically less than 2%).