Berend Markhorst

Berend Markhorst

he/him

PhD Candidate Operations Research @ CWI & VU Amsterdam

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Posts

portfolio

publications

A data-driven digital application to enhance the capacity planning of the covid-19 vaccination process

Published in MDPI Vaccines, 2021

In this paper, a decision support system (DSS) is presented that focuses on the capacity planning of the COVID-19 vaccination process in the Netherlands. With the Dutch national vaccination priority list as the starting point, the DSS aims to minimize the per-class waiting-time with respect to (1) the locations of the medical hubs (i.e., the vaccination locations) and (2) the distribution of the available vaccines and healthcare professionals (over time). As the user is given the freedom to experiment with different starting positions and strategies, the DSS is ideally suited for providing support in the dynamic environment of the COVID-19 vaccination process. In addition to the DSS, a mathematical model to support the assignment of inhabitants to medical hubs is presented. This model has been satisfactorily implemented in practice in close collaboration with the Dutch Municipal and Regional Health Service (GGD GHOR Nederland).

Recommended citation: Markhorst, B.; Zver, T.; Malbasic, N.; Dijkstra, R.; Otto, D.; van der Mei, R.; Moeke, D. A Data-Driven Digital Application to Enhance the Capacity Planning of the COVID-19 Vaccination Process. Vaccines 2021, 9, 1181. https://doi.org/10.3390/vaccines9101181 https://www.mdpi.com/2076-393X/9/10/1181

Sailing through uncertainty: ship pipe routing and the energy transition

Published in Proceedings of 15th International Marine Design Conference (IMDC 2024), 2024

The energy transition from fossil fuels to sustainable alternatives makes the design of future-proof ships even more important. In the design phase of a ship, it is uncertain how many and which fuels it will use in the future due to many external factors. In fact, a ship typically sails for decades, increasing the likelihood that it will use different fuels during its lifetime. Pipe route design is expensive and time-consuming, mainly done by hand. Motivated by this, in previous research, we have proposed a mathematical optimization framework for automatic pipe routing under uncertainty of the energy transition. In this paper, we build on the state-of-the-art by implementing design constraints in mathematical models based on discussions with maritime design experts. Additionally, we apply these models to realistic, complex situations of a commercial ship design company. Our experiments show that location-dependent installation costs, which reflect reality, increase the usefulness of stochastic optimization compared to deterministic and robust optimization. Additionally, to prepare for a possible transition to more sustainable fuels, we recommend installing suitable pipes near the engine room upfront to prevent expensive retrofits in the future.

Recommended citation: Markhorst, B. T., Berkhout, J., Zocca, A., Pruyn, J. F. J., & Van der Mei, R. D. (2024, May). Sailing through uncertainty: ship pipe routing and the energy transition. In International Marine Design Conference.

A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems

Published in Submitted to Networks, 2024

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm (“Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems”), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.

Recommended citation: Markhorst, B., Leitner, M., Berkhout, J., Zocca, A. & van der Mei, R. (2023). A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems. arXiv preprint arXiv:2412.10098. https://arxiv.org/abs/2412.10098

Future-proof ship pipe routing: navigating the energy transition

Published in Ocean Engineering, 2024

Ship pipe route design is often overlooked in the context of the energy transition, although it is a crucial driver for design time and costs. Motivated by this, we propose a mathematical approach for modeling uncertainty in pipe routing with deterministic optimization, stochastic programming, and robust optimization. The uncertainty entails not knowing which type of fuel will be used in the ship’s future. All three models are based on state-of-the-art integer linear programming models for the Stochastic Steiner Forest Problem and adjusted to the maritime domain using specific constraints for pipe routing. Our results highlight the importance of accounting for uncertainty in ship pipe routing, demonstrating cost reductions of up to 22% based on experiments with artificial and realistic data. Our methods enable engineers to explore different levels of preparedness for the energy transition with minimal effort during the early design phase.

Recommended citation: Markhorst, B., Berkhout, J., Zocca, A., Pruyn, J., & van der Mei, R. (2025). Future-proof ship pipe routing: Navigating the energy transition. Ocean Engineering, 319, 120113. https://www.sciencedirect.com/science/article/pii/S0029801824034516

Optimizing Mobile Stroke Unit Deployment: A Strategic Case Study In The Greater Oslo Area

Published in To appear in European Stroke Journal, 2025

This study examines the optimal placement of a Mobile Stroke Unit (MSU) in the greater Oslo area to maximize patient coverage and improve stroke treatment times. Using historical stroke data and a mathematical optimization model based on the Maximum Coverage Location Problem (MCLP), we identified the best MSU base location. Our findings suggest that optimal placement could increase patient coverage by 17%, and a rendezvous approach could further boost coverage by 300% for confirmed stroke cases. Additionally, the MSU could reduce time to thrombolysis by 27 minutes (25%) and time to thrombectomy by 35 minutes (20%). The study highlights the value of geospatial analysis in strategic MSU deployment to enhance prehospital stroke care and patient outcomes.

Recommended citation: Markhorst, B., Jagtenberg, C., Ranhoff Hov, M., Van der Mei, R. & Larsen, K. (2025). Optimizing Mobile Stroke Unit Deployment: A Strategic Case Study In The Greater Oslo Area https://journals.sagepub.com/home/eso

talks

teaching

Supervision experience

Thesis supervision, VU (mathematics department) and CWI (stochastics department), 2022

List of BSc and MSc students that I (co)supervise(d):

  • Emma Cornielje (2025): TULIP 2.0: Combining scenario reduction and Lagrangian relaxation to speed up two-stage stochastic mixed-integer linear programs - MSc Mathematics VU Amsterdam (together with dr. Alessandro Zocca)
  • Chris Vlak, Emma van Middendorp, Levi Biessen, Petra Katic, Yossi Hartman (2022): KLM Cargo delivery - BSc Business Analytics VU Amsterdam (together with prof. dr. Ger Koole)