Resilience in Interdependent Infrastructures: A Bilevel Optimization Approach to Coordination of Healthcare Networks

Contact Person: Gabriela Ciolacu

Target:

• Students with interest in game theory & bilevel optimization
• Students with interest in robust and/or stochastic optimization

Background and Motivation: Critical infrastructure networks do not exist in a vacuum, as their performance during routine and adverse event operations is often interdependent. For instance, a failure in one network can propagate through other networks that were otherwise unaffected and undermine the entire critical infrastructure’s capacity to respond to the event. Health systems are particularly susceptible to such propagating adverse events; namely, hospitals’ capacity to treat patients depends on medical supply chains, transportation systems, and energy grids. While policy discourse often assumes that more coordination among these interdependent networks improves resilience, this assumption may not always hold.  Recent work on coordination before and after adverse events shows that coordination is not unconditionally beneficial. Especially among institutions of different power levels, resilience following an adverse event may depend on incentive mechanisms that encourage truthful reporting. Additionally, the coordination structure can also influence network resilience (e.g., how sub-groups of hospitals coordinate instead of a network-level pooled resource; how blood banks coordinate with hospitals). This thesis aims to understand the interrelationship between coordination and resilience in the context of adverse events and uses healthcare networks as a contextual application. The student may explore whether they want to delve deeper into the coordination structure (e.g., capacity-sharing rules, coalition formation rules, patient-reallocation rules) or the incentive mechanism (e.g., rewards, penalty schemes, contract mechanisms) that enhances resilience. Both avenues of research are possible, but it is advised to choose one. 

Relevant Literature:

• Adsanver, B., Balcik, B., Bélanger, V., Rancourt, M.È., 2024. Operations research approaches for improving coordination, cooperation, and collaboration in humanitarian relief chains: A framework and literature review. European Journal of Operational Research 319, 384–398.
• Tippong, D., Petrovic, S., Akbari, V., 2022. A review of applications of operational research in healthcare coordination in disaster management. European Journal of Operational Research 301, 1–17

Coordination mechanisms:

• Parsa, I., Eftekhar, M., Webster, S., & Van Wassenhove, L. N. (2026). Analyzing coordination structures for effective humanitarian relief operations. Scientific reports, 16(1), 1327.
• Hosseinifard, Z., Abbasi, B., 2018. The inventory centralization impacts on sustainability of the blood supply chain. Computers & operations research 89, 206–212.

Incentive mechanisms:

• Paul, A., Rajapakshe, T., Mallik, S., 2019. Socially optimal contracting between a regional blood bank and hospitals. Production and Operations Management 28, 908–932.
• Liang, Y., Sun, P., Tang, R., Zhang, C., 2023. Efficient resource allocation contracts to reduce adverse events. Operations Research 71, 1889–1907.
• Toyasaki, F., Arikan, E., Silbermayr, L., & Falagara Sigala, I. (2017). Disaster relief inventory management: Horizontal cooperation between humanitarian organizations. Production and Operations Management, 26(6), 1221-1237.

Synthetic data generation methods for hospital operations

Contact Person: Gabriela Ciolacu

Target:

• Bachelor students.

Motivation: Synthetic data generation has emerged as a promising alternative to overcome data scarcity and privacy challenges in the healthcare sector. Synthetic healthcare data is used in multiple disciplines (e.g., computer science, public policy) for diverse purposes, such as training machine learning models for use cases where data about a particular incident (e.g., a disaster, a rare variation of COVID-19) is limited.

In operations research (OR), synthetic healthcare data is still novel. However, synthetic data is not used to assess and evaluate the impact of an intervention (e.g., a new inventory management policy or a new plan for emergency response in case of a disaster). Such purpose is rather reserved for simulations, and simulations can be used to produce synthetic data. In OR, the goal of synthetic data is to evaluate and validate the performance of an optimization algorithm (e.g., for a hospital or medical unit). An exemplary OR use case focuses on generating hospital operational data to train a model. We propose this thesis to better understand its uses for OR and subsequent generation methods.

This thesis aims to synthesize literature on the available syntenic data generation use cases and methods that can be used to replicate hospital operational data, such as resource distribution. Exemplary resources can be nurses, surgeons, or surgical supplies. Based on the generated synthesis, it is also expected to showcase means to evaluate the validity of such synthetic data in each OR use case context.

Operations research related literature:

• Brailsford, S. C., Eldabi, T., Kunc, M., Mustafee, N., & Osorio, A. F. (2019). Hybrid simulation modelling in operational research: A state-of-the-art review. European Journal of Operational Research, 278(3), 721-737.
• European Journal of Operational Research, 315(3), 863-878. – Example of synthetic data generation for  OR purposes Production & Manufacturing Research, 10(1), 337-353. – Example of synthetic data generation for a manufacturing plant

Healthcare related literature:

• Giuffrè, M., & Shung, D. L. (2023). Harnessing the power of synthetic data in healthcare: innovation, application, and privacy. NPJ digital medicine, 6(1), 186.
• PLOS Digital Health, 2(1), e0000082. – This is an introductory literature review about possible cases of use for synthetic healthcare data. BMC Medical Research Methodology, 23(1), p.67.

Requirements:

• Desired understanding of at least one programming language (e.g., Python). Not required.

Modeling and Predicting Hospital Demand

Contact Person: Gabriela Ciolacu

Target:

• For bachelor students, we require a literature review (e.g., structured or unstructured).  A numerical investigation is also desired, but it is not compulsory.
• For Master students, we would require additional numerical investigation(s).  For instance, it is expected of the student to model the demand in a hospital, based on an identified dataset and aim to predict the demand following the findings of the literature review. It is expected to showcase and compare 3+ forecasting methods.

Motivation:

Hospitals are often subject to uncertainty, such as natural or human-caused disasters. Hence, accurately predicting hospital demand could assist in better preparedness against such uncertainty, such as allocating resources to avoid possible stock breakdowns or overstocking, ensuring resource availability at reasonable costs within the budget, and providing continuous patient care. However, predicting stochastic demand under uncertainty is not a simple task. For instance, surgeries in a hospital can run longer than expected due to unforeseeable complications from the patient’s conditions, or staffing or equipment may become limited due to unexpected mass casualties. For other medical units, this might not be the case. Such variability makes it challenging for decision-makers to strategically plan and budget their expenses, respond to seasonal trends, or aim to optimize resources.

This thesis aims to synthesize literature on the available methods to predict hospital demand. For instance, it is expected to deliver an overview of the predictive methods per hospital unit (e.g., operating room, emergency department) that include uncertainty and those that do not consider it (e.g., differentiate between deterministic and stochastic demand modeling). This thesis must be centered around hospital demand in uncertain scenarios (e.g., before a disaster), focusing on operations research. Based on the generated synthesis, an analysis of the methods is expected. For example, the thesis will also offer a critical analysis of use cases, specific objectives, the benefits of those methods for the applied use cases, performance measures, and limitations.

Literature:

• Barros, O., Weber, R., & Reveco, C. (2021). Demand analysis and capacity management for hospital emergencies using advanced forecasting models and stochastic simulation. Operations Research Perspectives, 8, 100208.
• Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
• Gul, M., & Celik, E. (2020). An exhaustive review and analysis on applications of statistical forecasting in hospital emergency departments. Health Systems, 9(4), 263-284.

Requirements:

• Solid understanding of time series analysis and forecasting.
• Desired knowledge in machine learning.

Multiobjective Vulnerability Assessment of Networks under Joint Node and Link Attacks

Contact Person: Stephan Helfrich

Target:

1. Master students with Background in Optimization Theory

Motivation: Critical infrastructures, such as the information technology systems of hospitals or transportation networks, are highly vulnerable to malicious attacks and natural disasters. Therefore, it is essential to identify critical components whose removal or attack would severely disrupt the system. This can be achieved by formulating and solving the β-disruptor problem, an optimization problem that aims to identify a minimum-cost set of links and nodes in a network whose removal would disrupt network connectivity up to the threshold β.

The goal of this thesis is to study the multiobjective variant of the β-disruptor problem, where the connectivity threshold β is treated as the second objective. This approach provides insights into the trade-offs between vulnerability and costs and reveals additional structural insights into the interdependencies within the critical infrastructure.

Subject of studies are but not limited to:

• Literature review of existing approaches to the β-disruptor problem and its variants
• Complexity analysis of the multiobjective disruptor problem with respect to, for example, tractability and output-sensitivity
• Design of multiobjective exact algorithms
• Design of multiobjective approximation methods with worst-case guarantees on running time and solution quality
• Design of multiobjective heuristic methods
• Implementation and performance analysis of derived methods

Literature:

β-disruptor problem:

• T. N. Dinh and M. T. Thai (2015) Network Under Joint Node and Link Attacks: Vulnerability Assessment Methods and Analysis. IEEE/ACM Transactions on Networking 23:3:1001-1011
• M. Lalou, M. Tahraoui, H. Kheddouci (2018) The Critical Node Detection Problem in networks: A survey. Computer Science Review 28:92-117

Multiobjective optimization:

• Ehrgott, M. (2008) Multicriteria Optimization (Springer Berlin, Heidelberg)
• A. Herzel, S. Ruzika, and C. Thielen (2021) Approximation Methods for Multiobjective Optimization Problems: A Survey. INFORMS Journal on Computing 33(4):1284-1299.
• Bökler F., Ehrgott M., Morris C., Mutzel P. (2017) Output-sensitive complexity of multiobjective combinatorial optimization. Journal of Multi-Critiria Decision Analysis 24: 25–36.

Requirements:

• Master students with Background in Optimization and basic complexity theory

Restoration Optimization for Improving Resilience of Critical Infrastructures

Contact Person: Stephan Helferich

Target:

• Bachelor and Master students with Background in Mathematical Optimization

Motivation:

Resilience is commonly understood as the ability of a system to plan and prepare for, absorb, respond to, and recover from disruptions, and to adapt to new conditions. It is therefore naturally expressed through several criteria, each addressing a different capability of a system (e.g., time to recovery, accumulated performance deficit, …) and/or phase of a disruption (resistance phase, absorption phase, recovery phase) (Cheng, Elsayed, and Huang, 2021).

Recent work formalizes resilience as a multicriteria optimization problem and presents an optimization model for preparedness actions that can be committed before an adverse event to improve the resilience of the system (Helfrich, Ciolacu, Böckmann, and Grass, 2026).

In this framework, the decision content lies predominantly in the pre-event stage: preparedness actions are committed before the adverse event, whereas recovery is represented in stylized form rather than as the outcome of explicit restoration decisions (Ghorbani-Renani, González, Barker, and Morshedlou, 2020).

The goal of this thesis is to study restoration models in view of the multicriteria optimization perspective of resilience. It examines how restoration governs the recovery phase and how restoration decisions can be embedded into and optimized within the multicriteria resilience framework. In this way, the vulnerability and recoverability of such critical infrastructure systems can be assessed jointly, and pre- and post-disruption decisions evaluated and optimized within a common model.

Subjects of study are but not limited to:

• Literature review of restoration and recovery models covering complexity, solution algorithms, and applications, together with an overview of variants of these problems.
• Literature review and evaluation of resilience criteria and their applicability to restoration.
• Design of a restoration optimization model that renders recovery an outcome of explicit restoration decisions and integrates it into the multicriteria resilience framework.
• Implementation and numerical study of existing restoration models based on artificial instances used in the literature.
• Design of new exact and/or approximate solution algorithms for restoration within the multicriteria resilience framework.
• Application of the algorithms to restoration planning for disrupted networks, for example the recovery of hospital networks following a cyberattack.

Literature:

• Cheng, Y., Elsayed, E. A., & Huang, Z. (2021). Systems resilience assessments: a review, framework and metrics. International Journal of Production Research, 60(2), 595–622. https://doi.org/10.1080/00207543.2021.1971789
• Ghorbani-Renani, N., González, A. D., Barker, K., & Morshedlou, N. (2020). Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience. Reliability Engineering & System Safety, 199, 106907. https://doi.org/10.1016/j.ress.2020.106907
• Helfrich, Ciolacu, Böckmann, & Grass (2026). Resilience Optimization of Network Flows over Time (in preparation).

Defender-Attacker Optimization Models in Network Security

Contact Person: Stephan Helferich

Target:

• Bachelor (and Master students) with Background in Cybersecurity and Mathematical Optimization

Motivation:

Cyberattacks have evolved into one of the major threats to modern IT infrastructures. They are becoming more frequent, increasingly sophisticated, and more difficult to prevent, while their operational and economic consequences continue to grow. This highlights the need for organizations to allocate their (typically limited) resources so as to protect their IT infrastructure and information assets against adversarial attackers as effectively as possible. Decision support for this task can be provided through attacker-defender optimization models, which represent the interaction between defender and attacker as an optimization problem and thereby identify how limited defensive resources should be allocated in view of the attacker's best response (Hunt, Zhuang (2024).

Any such model, however, requires a representation of what the attacker can actually do. Threat modelling techniques, such as attack trees and attack graphs, provide structured representations of these possibilities. They combine information about network topology (hosts, connectivity, and trust relationships) with information about individual components (services, configurations, and detected vulnerabilities) to represent possible sequences of actions an attacker may take to compromise a system (Zenitani (2023)). Integrating such threat models into attacker–defender optimization therefore provides a principled basis for cybersecurity decision support.

The goal of this thesis is to survey approaches that connect attacker-defender optimization with threat modelling techniques. It reviews the relevant threat modelling techniques, classifies how they are embedded into attacker-defender optimization models, compares the resulting formulations and solution methods, and identifies their strengths, limitations, and open directions.

The subjects of study include, but are not limited to:

• Literature review of threat modelling techniques relevant to optimization and of attacker-defender optimization models built on these threat models
• Classification of how threat models are embedded into optimization: what the attacker optimizes (for example likelihood, effort, or impact), what the defender decides (controls, patches, or budget), and how the two levels are coupled.
• Overview and comparison of solution methods and review of application domains and case studies in which such coupled models support cybersecurity decisions.
• Discussion of limitations and open directions, for example handling uncertainty in the threat model or extending to richer objectives.
• Master students are expected to additionally implement and extend selected attacker–defender models and to numerically evaluate their solution quality, computational performance, and scalability.

Literature:

• Zenitani, K. (2023). Attack graph analysis: An explanatory guide. Computers & Security
• K. Hunt and J. Zhuang: A review of attacker-defender games: Current state and paths forward. European. Journal of Operational Research 313(2): pp. 401–417.