## 3 Methods  
### Use Case Creation  
In order to create a realistic use case to share with the HHCRSP scientific community, the staff at seven home health care or service structures were interviewed in the department of Tam in France during the months of September and October 2022. The aim was to collect information on the working environment, e.g., operating methods, problems encountered, existing and envisaged solutions, tools used, needs, etc. Having identified the challenges of the home care centers, we decided to create a use case inspired by two of these nursing care structures, which have the following characteristics:  
1. There are five caregivers performing five routes;
2. Routes start at 7 a.m. from the health care center and end between 12 p.m. and 1 p.m. at the same location;
3. There are 140 care visits to perform, which are requested by 140 patients (one visit per patient);
4. When the caregivers have finished their routes, they can help their colleagues, if needed, or do administrative tasks at the health care center until 1 p.m.;
5. Travel times are often short (usually less than five minutes) and are triangularly distributed more or less 30% around the average value;
6. Care visit times are generally five minutes but can sometimes last 10 min. They are both subject to variations (such as travel times, with the same distribution) and to disruptions (whose distribution is detailed in the design of experiments);
7. Time windows (i.e., time slot during which the caregiver must begin the care visit) last one hour for each visit;
8. There is an early and late tolerance of five minutes, and if the caregiver arrives more than five minutes early, then they must wait before starting the care visit;The website \"[[https://geodatamine.fr/](https://geodatamine.fr/)]([https://geodatamine.fr/](https://geodatamine.fr/)) (accessed on 7 February 2023)\" was used to generate random and unidentifiable addresses for patients (e.g., businesses, churches, parking spaces, etc.) around the city of Carmaux (France); the map is presented in Figure 2 on the left (1) where the library _folium_ in Python was used to place the patients on a Leaflet map. The health care center was indicated in the city, and the 140 other addresses were randomly distributed to the patients. The website \"[[https://openrouteservice.org/](https://openrouteservice.org/)]([https://openrouteservice.org/](https://openrouteservice.org/)) (accessed on 7 February 2023)\" was used by a query in a Python script to create a matrix of real travel times between patients.  
There are two types of visits: the short visits of 5 min, which represent 75% of the visits, and the long visits lasting 10 min (Figure 2, (2)). Thus, 106 care visits last 5 min, distributed randomly among the patients, and the other 34 last 10 min.  
Finally, the time windows must be determined for each visit (Figure 2, (3)). There are 11 possible time windows between 7 a.m. and 1 p.m. (7 a.m.-8 a.m., 7:30 a.m.-8:30 a.m., 11:30 a.m.-12:30 p.m., and 12 p.m.-1 p.m.), evenly distributed among the visits in order to find feasible and realistic solutions.  
The map, the coordinates of the addresses, and the care visits file are available in the data archive available at \"[[http://dx.doi.org/10.13140/RG.2.2.28201.98402](http://dx.doi.org/10.13140/RG.2.2.28201.98402)]([http://dx.doi.org/10.13140/RG.2.2.28201.98402](http://dx.doi.org/10.13140/RG.2.2.28201.98402)) (accessed on 15 May 2023)\" (Supplementary Material).