This idea naturally lends itself to a clustering problem such as k-means! We can imagine a geographical density as a cluster and that semi centralized pickup point as a centroid. As for deciding k, the number of cluster-centroid pairs, we can leave that up to market prices.

One way to adapt the k-means algorithm to this would be to add a “regularizing” or penalizing term proportional to the number of cars needed to be deployed — you can think of this as the cost per car.