In this work, we present the solution approach for the Integrated Healthcare Timetabling Competition 2024 submitted by Team Twente, which ultimately ranked third among the finalists. Our approach combines mixed-integer programming, constraint programming, and simulated annealing in a 3-phase solution approach based on decomposition into subproblems. In addition to describing our approach and design decisions, we share our insights and, for the first time, lower bounds on the optimal solution values for the benchmark instances. We analyze the results based on solution quality for the competition and an extended runtime Additionally, we investigate the different soft constraints and specific parts of the algorithm. Finally, we highlight open problems and future research directions for further improving the approach.
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