# Generating Activity-Based Mobility Plans from Trip-Based Models and Mobility Surveys
## 3 Materials and Methods
### Approach
#### 3.3.3 Assign Activity Locations
Equation (1) is a modified version of the formula introduced by [PERSON] et al. [5], who also determined activity locations based on a multinomial logit model that employs driving willingness and TAZ attraction. In contrast to their  
Figure 5: Schematic illustration of the process of generating driving willingness distributions. Figure 6: Observed driving willingness (original weighted data) and fitted distributions with the best fit. version, the mobility behavior conformance term \(conf_{j||p}\) expresses how likely it is that one would drive at least the distance \(d_{ij}\) to conduct activity type \(p\). The conformance term is based on \(f_{p}^{D}\) and \(F_{p}^{D}\), which are the PDF and cumulative distribution function (CDF), respectively, of the driving willingness distribution. \(D\) is the random continuous distance variable of these functions. The distribution type and parameters are specific to each activity type \(p\) and result from the distribution fitting process, and \(att\) is the TAZ-specific attraction, which corresponds to the number of places in a TAZ, where activity \(p\) can be performed, which was taken from MITO in our application. Meanwhile, \(d_{ij}\) is the road distance between the centroids of TAZ \(i\) and \(j\), approximated by the direct line distance \(\overline{d_{ij}}\) and \(a_{\text{dist}}\), a constant factor to approximate the road distance based on the direct line distance that is used to avoid routing and hence reduce the model complexity. In reality, the selection of activity locations is a trade-off between the benefit of visiting a location and the effort of getting there [5]. Equation (1) models this behavior by rewarding an attractive TAZ (\(att\)) and penalizing long distances (\(conf\) decreases with an increasing distance). [PERSON] et al. [5] penalized the displeasure of transport by an exponential distance function. Hence, short distances are strictly favored over long distances. Our methodology, however, applies the probability of driving at least the considered distance. This models the trip's conformance with observed mobility behavior, which decreases with the distance. The probability is calculated by integrating the driving willingness PDF over the interval from the considered distance to infinity. This slightly different approach was chosen to enforce that the simulated driven distances followed the same distribution as the underlying general mobility survey and allow different activity types to have different distribution types. This came at the cost of not modeling a human desire: the location choice was not constrained by the displeasure of driving but was statistically remodeled based on the observed distributions. This is more similar to trip-based methods than activity-based methods. Following the assignment of the main activities' locations, the secondary activities' locations were assigned. The process for secondary activities differs from the one for main activities. This employs a concept of detour willingness instead of driving willingness while simultaneously respecting that there may be multiple secondary activities instead of a single main activity. As with driving willingness distributions, detour willingness distributions are used to quantify the willingness of persons to take a detour of a certain distance off of the direct route between home and a main activity to conduct a secondary activity. In our approach, detour willingness distributions were determined using the same distribution fitting approach as that for the driving willingness distributions. For each activity type \(p\) occurring as a secondary activity, one PDF \(f_{\text{detour},p}^{D}(d,parameters_{p})\) of a detour distance \(d\) over a continuous random distance variable \(D\) is created. This willingness was assumed to depend solely on the activity type of the considered secondary activity. The detour willingness of activity type \(p\) is derived from triangular trips \(\overline{ijji}\) originating from and ending at home \(i\).