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LOTUS: A Warm-Start Framework for Powering Dual Decomposition in Large-Scale Two-Stage Stochastic Programs

Published in arXiv preprint, 2026

Solving large two-stage stochastic mixed-integer programs is computationally challenging. We propose LOTUS, a subset-based warm-start framework that enhances Dual Decomposition under fixed time budgets. By initializing the dual search with informed multipliers, LOTUS accelerates primal convergence and partially alleviates the impact of weak LP relaxations. Through an extensive computational study on production planning instances, we show that, within two hours, LOTUS yields significantly better primal solutions in 45.83% of cases, while being outperformed by Dual Decomposition in only 4.17%.

Recommended citation: Cornielje, E., Markhorst, B., Zocca, A., & van der Mei, R. (2026). LOTUS: A Warm-Start Framework for Powering Dual Decomposition in Large-Scale Two-Stage Stochastic Programs. arXiv preprint arXiv:2603.01733. https://arxiv.org/abs/2603.01733

A Fast Heuristic for Stochastic Steiner Tree Problems

Published in arXiv preprint, 2026

Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem, there are considerably more state-of-the-art heuristics for its deterministic variant, the Steiner Tree Problem (STP). In this work, we show how to leverage an existing STP heuristic in building a novel method for solving its stochastic variant, the SSTP. This approach is a powerful, yet simple and easy-to-implement way of solving this complex problem. We test our method using benchmark instances from the literature. Numerical results show considerably faster computation times compared to the state-of-the-art, with a gap of approximately 5%.

Recommended citation: Markhorst, B., Zocca, A., Berkhout, J., & van der Mei, R. (2026). A Fast Heuristic for Stochastic Steiner Tree Problems. arXiv preprint arXiv:2602.23858. https://arxiv.org/abs/2602.23858

Optimizing gas entry-exit capacity utilization under uncertainty

Published in Computational Management Science, 2026

Natural gas is vital to Europe’s energy system, with Norway supplying 30% of European gas demand. Effective management of entry-exit capacity in the Norwegian network can enhance market efficiency and energy security, but is far from trivial due to uncertain demand and prices. This study develops a stochastic programming model to determine optimal capacity allocation under uncertainty, with a focus on scalability. Concerned about network stability, operators tend to be risk averse in deviating from their initial decisions when allocating bookable capacities. We use our model in a case study on Norway’s gas pipeline network and find that moderating risk aversion can yield considerable system welfare gains. Additionally, we give insights into the system bottlenecks for policymakers and industry stakeholders and show the value of flexibility in this context. Finally, we provide a comprehensive dataset to advance future research.

Recommended citation: Markhorst, B., Buijs, R., Egging-Bratseth, R. & Van der Mei, R. (2026). Optimizing gas entry-exit capacity utilization under uncertainty. Computational Management Science. Volume 23, article number 9 https://link.springer.com/article/10.1007/s10287-025-00552-3

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

Published 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., Hov, M. R., van der Mei, R., & Larsen, K. (2025). Optimizing mobile stroke unit deployment: A strategic case study in the greater Oslo area. European Stroke Journal, 23969873251329862. https://journals.sagepub.com/doi/full/10.1177/23969873251329862

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

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

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 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

Berend Markhorst

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