## 4 Overview and Functioning of the Generator
### Listing and Range of All Parameters
#### 4.2.2 Editable Parameters  
Firstly, to setup up a benchmark correctly, the first parameter allows the generator to produce more than a unique instance following the current configuration. Some data are generated randomly such as the distance between patients or compatibilities. However, some can be similar between two instances such as the number of caregivers/patients or several proportions. The second parameter of an instance is the geographical boundary of the instance. Those coordinates enable the generator to set up different coordinates in the designated area for caregivers, patients, and depots. As explained earlier, distances are calculated by following a straight line between two patients/depots. Usually, studies [13; 31; 34] have been based on a daily planning horizon, but the third parameter allows the generator to set a different number of days in the planning horizon. Depending on how the HHCRSP is treated, the number of days can be one day for a short-term plan or two to seven days for a mid-term plan. Long-term planning is not taken into account due to its marked difference with short- and mid-term planning. The number of patients and caregivers has a huge impact on how jobs are generated. Indeed, several studies [6; 23; 25; 39] concluded that a patient may have on average three to four jobs (cares) per day. A caregiver is also able to deal with six to seven jobs per day depending on how much time a job needs to be performed properly [5; 11; 21; 30]. Qualifications and skills are important to define different types of jobs in an instance [9; 13; 34; 41]. The HHC literature has concluded the fact that all feasible jobs met in an HHC center can be categorized into six major qualifications on average. The HHC literature also presents two distinct ways to tackle the qualification constraint [9; 16; 22]. The first approach considers all skills as mutually independent. This approach is often met when the HHC center deals with a wide array of jobs (palinative care to daily care). The second approach is based on a pyramidal scheme. For example, a caregiver who possesses a specific qualification \(Q_{i}\) automatically possesses all qualifications at a lower level. The second approach is usually used in HHC problems with a huge VRP component [9; 12; 40]. The generator implements the first approach and uses independent qualifications. To ensure continuity of care, studies in the literature implement a reference caregiver [42]. During the scheduling process, a reference caregiver is more likely to be assigned to his/her reference patient if it is possible to ensure a partial continuity of care. As explained in the previous section, caregivers can have different labor agreements (full-time or part-time), so the next parameter allows the generator to set up different proportions of part-time caregivers. This ratio can vary from a small portion to half of the number of caregivers. The traveled time parameter is an optional parameter. It measures \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameters** & **Range** & **References** \\ \hline Range of duration & 30–90 min & [13; 15; 29] \\ Range of the time frame to proceed with the job & 1–2 h & [9; 13] \\ Range of the time frame between one job and another job & 2 h & [12; 13; 40] \\
\begin{tabular}{l} Range of arduousness/priority score \\ \end{tabular} & 0–3 & [13; 22] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Range of non-editable parameters for jobs. how much time caregivers are on the road. On average, this time may be around 18% to 25% of their working time [13; 33]. This parameter has a huge influence on how jobs are generated because the generator takes into account this percentage to create jobs in order to not overload the HHC center. The time traveled parameter is heavily linked to the next parameter: the occupation or saturation rate of instance. This parameter is the ratio between the number of working hours generated by all jobs and the number of working hours available in the HHC center.