## 2 Problem Definition  
We focus on the problem that a municipality deals with when it must choose the locations of lots to be rented for the parking shared e-scooters inside its administrated territory. Commonly, such territory is partitioned into a set of districts \(D\) and, in turn, every district \(d\in D\) is partitioned into a set of subdistricts \(S(d)\) (see Figure 1 for a real-world example). We also introduce the set of all subdistricts \(S\), defined as \(S=\cup_{d\in D}S(d)\) and we remark that any subdistrict belongs to one single district. Within a subdistrict \(s\) belonging to a district \(d\), the municipality identifies the locations of a set of potential parking lots \(L(d,s)\), among which the activated and deployed ones are chosen. Each lot \(\ell\in L(d,s)\) is characterized by the number \(n_{ds\ell}\) of e-scooters that it may host. Such a number depends on the size of the lot and we remark that each lot must be rented as a whole (no fraction of places can be rented). Each lot is also associated with a value \(v_{ds\ell}\) that reflects the economic benefits of making it available to sharing services. When choosing which lots to rent, a municipality typically takes into account a lower bound \(\mathrm{LBTOT}\) and an upper bound \(\mathrm{UB}^{\mathrm{TOT}}_{ds}\) on the total number of parking places that are made available to the sharing services in each subdistrict \(s\) of a district \(d\). This takes into account the size of the fleets of sharing companies (for example, in the case of Rome, Italy, at most 3000 shared e-scooters are allowed to be deployed in the entire city by each of the three companies that operate in the city [27]). Furthermore, an important aspect to take into account when modeling the rental problem is that not all the candidate lots identified by the municipality may be rented at the same time: these reserved lots \"steal\" space from other parking lots, in particular, those reserved for cars, and this may lead to discontent among local residents. We indeed consider the case in which the lots are positioned directly on the street, in order to avoid e-scooters riding on sidewalks for parking (riding on sidewalks constitutes a relevant source of risks for pedestrians). The discontent of residents is especially expected in cities congested with cars, where finding an empty parking lot may be problematic and cruising time for parking search tends to be high (this is the case of the Italian city of Rome, which we consider as a test case in our computational study). For modeling this, we first introduce a value \(c_{ds\ell}\) that indicates the number of car parking places that are occupied by a lot \(\ell\) and we then introduce an upper bound \(\mathrm{UB}^{\mathrm{c}}_{ds}\) denoting the highest number of car places that can be subtracted by e-scooter parking lots in each subdistrict \(s\) of a district \(d\). This limit could and should be defined in concentration with local residents and, for example,  
Figure 1: Visualization of the administrative division of the territory of Rome (“Municipi” and “Zone Urbanistiche”). (**a**) Districts of Rome, (**b**) Subdistricts of Rome. could be defined as a (very) small fraction of the total number of car places available in the subdistrict. Finally, we consider the possibility for the municipality to classify all the potential lots according to classes: for instance, the class of a lot \(\ell\) could be established by taking into account the number \(n_{ds\ell}\) of places that \(\ell\) hosts; as an alternative, as we have discussed with professionals of shared micromobility, the municipality could classify lots according to the nature of its location (e.g., residential or business) and could aim at having a fair balance between larger and smaller lots in its districts.