## 2 Literature Review  
The HHCRSP is a highly pertinent issue and is widely studied in the literature, as evidenced by the numerous state-of-the-art published recently [6; 7]. In this section, we present an overview of the existing work to contextualize our contribution. HHCRSP problems cover a wide range of constraints and objectives. They may include typical features of Vehicle Routing Problems (VRPs), such as time windows (hard or soft) [8] and temporal dependencies (precedence, synchronization, or disjunction) [9], but also more specific features related to the field such as continuity of care [10], skill requirements [11], or incompatibilities [12]. The objective is often cost-related, whether it comes to minimizing travel costs or staffing costs [13; 14] or is stakeholder-oriented [8]. As a variant of VRP, approaches seeking to address the issues around HHCRSP are manifold. In small instances, exact methods are developed, e.g., mathematical programming [15], logic-based Benders decomposition [16], branch-and-price-and-cut [17], etc. Larger instances are generally solved with classic metaheuristics or approximation algorithms from the operations research field, such as population-based algorithms [18], neighborhood searches [19], and decomposition methods [20]. In practice, caregivers encounter various problems during their route that can impact the remainder of their working day. Hence, deterministic approaches do not enable us to capture the whole complexity of the HHCRSP, at least not at the operational decision making level. There are an increasing number of articles currently assessing the HHCRSP in view of various types of uncertainties (e.g., stochastic travel times or visit times, patient cancellations, emergencies, vehicle breakdown, etc.) and propose robust or resilient solutions: visits have an expected duration but can last longer [21] or they are normally distributed [11], and travel times are estimated with a kernel regression, for example [22]. In this paper, we focus on two forms of uncertainties regarding visit and travel times: small _variations_ due to the stochasticity of the data and more punctual but also more impactful _disruptions_, such as traffic jams. The robustness of a system is defined as the ability \"to maintain its function despite internal or external disruption\" [23], whereas resilience is \"the ability of a system to return to its original state, within an acceptable period of time, after being disturbed\" [24]. A _robust_ solution is, therefore, used to absorb a _variation_, and a _resilient_ approach is used to counter _disruption_. As represented in Figure 1, a robust solution in blue on the left absorbs the variations (represented by \(\sigma\) in orange) around the mean value \(\mu\), so these variations do not affect the performance indicators on the bottom, which are protected by this solution. On the right, the disruption has an impact on these indicators, and that is why a resilient approach is necessary to return to a \"normal\" operating state. These uncertainties can be addressed at different decision-making levels. [PERSON] et al. propose a two-stage stochastic programming model to tackle both uncertain visit and travel times [25], and [PERSON] et al. propose a mixed-integer linear program and adapt the L-shaped method to solve the HHCRSP with stochastic visit times [26]. Another option to deal with uncertainties is to anticipate different disrupted scenarios and build robust solutions; in the study by [PERSON] et al., each visit and travel time belongs to an uncertainty set based on the theory of budget uncertainty [27]. Since their solutions to the deterministic problem are not robust, they adapt several classic heuristics to build a solution that always remains feasible, despite visit and travel time uncertainties. [PERSON] et al.