DIAMANT-STAR: Stochastics meets Optimization

Organisers: Onno Boxma (TU Eindhoven), Frits Spieksma (TU Eindhoven)

Ward Romeijnders (University of Groningen)

Convex approximations for mixed-integer stochastic programs.

We consider two-stage mixed-integer stochastic programs. These optimization problems are notoriously difficult to solve since they combine the difficulties of having random parameters and integer decision variables in linear programming problems. For this reason, we do not aim to solve these problems exactly, but instead construct convex approximations for these problems. To guarantee the performance of the resulting approximating solutions, we derive error bounds for the convex approximations. The error bounds are smaller if the variability of the random parameters in the model is larger.

Stella Kapodistria (TU Eindhoven)

Exact and approximate solutions for a class of stochastic dynamic programming problems.

We consider a class of stochastic dynamic programming (SDP) problems arising in the context of maintenance. Such SDP problems aim at deriving optimal policies (when should maintenance be performed and by how much should the system be maintained). From a fundamental perspective, the difficulty of such SDP problems lies in deriving the optimal policy. From a numerical perspective, the difficulty lies in computing the policy (the curse of dimensionality). While, from a practical perspective, the difficulty lies in the stochastic modelling of all the relevant information (big data). In this talk, we present an overarching framework that aims at addressing all aforementioned challenges.