Healthcare systems are essential to society but face numerous challenges in maintaining their resilience and long-term viability. Disruptions, much like those experienced in supply chains-can significantly hinder operational continuity. To mitigate such risks, strategic investments can be made to reduce the likelihood of service interruptions. However, given the constraints of a limited protection budget, it is crucial to allocate resources efficiently to enhance the resilience of selected critical facilities. The objective of this research is to develop an optimal protection strategy that minimizes both patient travel distances for accessing care and the number of patients left without timely treatment due to disruptions. Since accurately predicting facility failures remains difficult, robust optimization provides a valuable framework. In particular, a scenario-based robust decision-making approach allows for the evaluation of multiple plausible disruption scenarios, ensuring that the selected strategy performs well under various conditions. Our methodology leverages scenario analysis to identify the most effective investment strategy for sustaining healthcare system performance over time. Each scenario corresponds to a different allocation of protective investments, and we assess their respective impacts on system resilience. By analyzing the relationship between the fortification of specific facilities and overall system performance, we generate insights to inform budget allocation decisions aimed at maximizing resilience. This process helps quantify the relative importance of each facility, enabling an optimized distribution of resources within fixed budgetary limits.

In recent years, climate change and health crises have multiplied, including the global pandemic of Covid-19. These crises have revealed the vulnerability of healthcare systems, but also their ability to adapt quickly and become resilient. However, this adaptation often comes at a cost. To address this problem, it is necessary to identify and prioritize measures to strengthen the current health system and make it more able to cope with future crises. One approach is to strengthen critical assets through effective investment strategies. The purpose of this study is to identify an optimal investment strategy to improve the reliability of health systems. We proposed a bi-objective investment strategy to strengthen healthcare systems against random disruptions. We contribute to the literature with a novel two-step modeling approach. First, we model the patient journey through the healthcare system as a Markov chain. The Markov chain allows us to capture the sequential nature of the patient journey and to analyze the probability of patient transitions between different stages in the system. Second, we have a bi-objective model mathematical model that calculates the optimal investment strategy based on the probabilities established earlier in order to minimize both patient travel distance and the number of patients waiting for care. The model and its computational results with a full enumeration approach are presented in the paper. The existence of a large number of facilities and investment levels increases the time needed to evaluate all solutions and find the optimal set of solutions. Therefore, it is important to consider the need for granularity in the investment levels when applied to real-world situations.