## 5 Test Cases
### Manhattan Test Instances  
Next to the above described purely artificial benchmark instances, we also derive benchmark instances from real-world yellow taxi trip data of Manhattan. As in CSS, MAN instances have two SPRs per use case. The underlying street network \(G\) of the instances corresponds to the street network graph of Manhattan provided by the Julia package LightOSM ([[https://github.com/DeloitteDigitalAPAC/LightOSM.j](https://github.com/DeloitteDigitalAPAC/LightOSM.j)]([https://github.com/DeloitteDigitalAPAC/LightOSM.j](https://github.com/DeloitteDigitalAPAC/LightOSM.j)), accessed on 10 June 2021). Taxi trips have been extracted from the 2016 Yellow Taxi Trip Data ([[https://data.cityofnewyork.us/Transportation/2016-Yellow-Taxi-Trip-Data/k67s-dv2t](https://data.cityofnewyork.us/Transportation/2016-Yellow-Taxi-Trip-Data/k67s-dv2t)]([https://data.cityofnewyork.us/Transportation/2016-Yellow-Taxi-Trip-Data/k67s-dv2t](https://data.cityofnewyork.us/Transportation/2016-Yellow-Taxi-Trip-Data/k67s-dv2t)), accessed on 10 June 2021). The taxi data set was first preprocessed by removing all trips with invalid data and trips made on a weekend. Furthermore, we have also removed all trips which do not start, as well as end, in Manhattan. For taxi trips within the months of January to July, geographic pickup and drop-off coordinates of customers are recorded in the data set. Each of these coordinates has been extracted and mapped to the geographically closest vertex in \(G\), resulting in a list of pairs of vertices \(Q\subseteq V(G)\times V(G)\). Next, as the similarity of users in our instances depends on their geographic proximity, we have reduced \(Q\) by considering only the ten taxi zones with the highest total number of pickups and drop-offs of customers, resulting in a total of approximately two million taxi trips. Geographic information of the taxi zones of Manhattan has been obtained from [[https://data.cityofnewyork.us/Transportation/NYC-Taxi-Zones/d3c5-ddgc](https://data.cityofnewyork.us/Transportation/NYC-Taxi-Zones/d3c5-ddgc)]([https://data.cityofnewyork.us/Transportation/NYC-Taxi-Zones/d3c5-ddgc](https://data.cityofnewyork.us/Transportation/NYC-Taxi-Zones/d3c5-ddgc)) (accessed on 10 June 2021). The left side of Figure 4 provides a visualization of the selected taxi zones. The set of potential service point locations \(V\) has been chosen randomly from vertices of \(G\) that are located in the considered taxi zones. The fixed costs \(z_{v}^{\text{fix}}\), as well as the variable costs \(z_{v}^{\text{var}}\), for setting up a service station at each location \(v\in V\), are uniformly chosen at random from \(\{50,\dots,100\}\). The number of use cases for each user \(u\in U\) is again chosen randomly according to a shifted Poisson distribution with offset one, expected value three, and a maximum value of five. Each of these use cases \(c\in C_{u}\) is associated with an individual demand \(D_{u,c}\) randomly chosen from \(\{5,\dots,50\}\) and the two SPRs representing the origin and destination of a trip chosen from \(Q\) uniformly at random. A rating for an SPR \(r\) is calculated for each \(v\in V\) via the sigmoidal decay function  
\[w_{r,v}^{\prime}=\frac{1}{1+10e^{0.01\text{sp}(r,v)}-6}, \tag{20}\]  
where \(\text{sp}(r,v)\) refers to the length of the shortest path between location \(v\) and the SPR \(r\) in the street network graph \(G\). The parameters of this function have been chosen in such a way that service point locations within a distance of approximately 600 meters to \(r\) are relevant for the SPR. Finally, the discretized suitability value \(w_{r,v}\) is again obtained by \(w_{r,v}=\left\lfloor 4\cdot\min(1,\max(0,w_{r,v}^{\prime}))+0.5\right\rfloor/4\). The right side of Figure 4 shows the distribution of SPR locations, as well as potential service point locations, as an example instance. The MAN benchmark group consists of 30 instances in total with each instance having 100 potential service point locations and 2000 users.