## 5 Modeling APL Systems
### Consideration of Customer Behavior  
For an overall comparison with respect to GHG contribution, the behavior of the customers, i.e., the emissions for picking up parcels at the APL, must also be taken into account. Here, a model is proposed to roughly estimate the additional CO\({}_{2}\) emissions. Depending on the distance to the APL, customers walk, take a bike, use public transport, or take a private vehicle to pick up their parcel at the APL. The behavior mainly depends on the distance to the APL and additionally the availability or--more generally--the typical usage of public transport within a certain area or district. Furthermore, a trip is either a single trip from the customer to the APL and back or the customer integrates the stop at the APL into an individual tour, also visiting other locations like shops, restaurants, or the customer's place of work. For the options of walking, taking a bike, or using public transport, the assumption is that no relevant additional CO\({}_{2}\) emissions have to be considered. In the case of public transport, of course emissions generally arise. In our model, however, we do not assume that new bus or train lines are opened or serve at a higher frequency in order to manage pickups at the APLs. Therefore, no additional CO\({}_{2}\) emissions have to be considered for public transport, and the focus lies on the usage of private vehicles. Here, an assumption  
Figure 6: Solution approach for determining and evaluation of APL system configurations. is required about the percentage of single trips and individual tours. Furthermore, the additional distance taken by the customer when visiting the APL on a tour with further stops has to be estimated. Here, the assumption is that the customer's tour is extended by the _fit_ percent of the direct distance to the packing station on average. The selection of the pickup option for the customers is implemented using a table indicating the probabilities for each pickup option depending on the distance to the APL (Table 1). Given the distance of the customer location to the assigned APL, the respective row is chosen according to column _until km_. Given the percentage _% foot or bike_, it is then randomly decided if the customer uses this option for picking up the parcel. If the option is not chosen, it is randomly determined whether the customer uses public transport. According to [60], from all customers that are not traveling by foot or bike, about 28% use public transport. In the cases of tours with the customers' own vehicles, it is finally randomly determined if they visit the APL with a single trip only for this pickup or during an individual tour combined with other tasks (column _% individual tour_). If an individual tour is selected, the additional VKT are calculated using parameter _fit_ as stated above. Otherwise, the VKT are twice the distance of the considered customer to the APL. As public transport is used to different degrees in the different districts within cities, a correction factor \(c_{i}\) for the percentage of customers using public transport in district \(i\) is introduced. Here, the results of a study for the city of Dortmund are used that evaluate the number of transportation methods people used per day (by foot, by bike, using individual vehicles, and using public transport) [60]. The average percentage of public transport was calculated compared to individual vehicles, and parameter \(cd_{i}\) is set as the respective factor for the individual deviation compared to the global average value of about 28%. Thus, the respective percentage in Table 1 can be changed, without the necessity to change the individual values for all districts for each scenario to be observed. A second correction factor \(cc_{k}\) is introduced for modeling the influence of the distance to the next public transport stop (bus or train) of a customer. Here, the respective data from OSM are used to determine the distance to the nearest public transport stop \(pt_{k}\) for each customer \(k\).