When trains are finished with their transportation tasks during the day, they are moved to a shunting yard where they are routed, parked, cleaned, subject to regular maintenance checks and repaired during the night. The resulting Train Unit Shunting and Servicing problem motivates advanced research in planning and scheduling in general since it integrates several known individually hard problems while incorporating many real-life details. We developed an event-based simulator called TORS (Dutch acronym for Train Shunting and Servicing Simulator), that provides the user with a state and all feasible actions. After an action is picked, TORS calculates the result and the process repeats. This simulator facilitates research into a realistic application of multi-agent path finding.@en

Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear relations in a compact human comprehensible model, by recursively splitting the population and predicting a distinct survival distribution in each leaf node. We use dynamic programming to provide the first survival tree method with optimality guarantees, enabling the assessment of the optimality gap of heuristics. We improve the scalability of our method through a special algorithm for computing trees up to depth two. The experiments show that our method’s run time even outperforms some heuristics for realistic cases while obtaining similar out-of-sample performance with the state-of-the-art.@en

A recent development in the field of discrete optimization is the combined use of (binary) decision diagrams (DD) and branch and bound for optimization. This method has been shown to outperform integer linear programming on several classic problems. The performance of DDs in integer optimization raises the question if this method can be extended to solve mixed integer problems (MIP), because of the prevalence of MIP modelling. This thesis is an effort to answer that question. Currently DD-based optimization does not allow for continuous variables. We propose a method that uses Benders Decomposition to divide MIP problems into a discrete master problem and a continuous subproblem. DD-based optimization is used to solve the master problem. The subproblem can be solved by linear programming. The results presented in this thesis show that our method can be used for MIP problems whose integer variables play a dominant role, and are hard to solve by MIP solvers. An advantage of our method is that it provides feasible solutions as early as the first iteration.