Collection and delivery points (CDPs) are fixed locations where customers can pick up parcels and/or drop off shipments or returns rather than requiring home delivery. CDPs allow logistics operators to consolidate multiple customer delivery requests on fewer vehicle stops, reducing distribution costs. However, for customers to adopt CDPs, they must be willing to travel to a nearby CDP to pick up their parcels. This choice depends on customers’ personal preferences, the proximity of CDPs, and economic incentives. To strategically size and plan cost-efficient CDP networks, we propose a continuous approximation model that jointly determines the optimal number of CDPs and the economic incentives offered to customers who choose to be served at CDPs, based on aggregated instance data. Furthermore, we equip our model with a chance constraint that limits the probability that the random demand associated with each CDP exceeds its design capacity. In our base experiment, we find that CDPs alone can cut expected distribution and infrastructure costs by 16.9%, while offering incentives to customers may increase potential savings to 28.0%. As an insight, we find that CDPs are most beneficial in high-density regions, where they leverage economies of scale, whereas incentives are more effective in low-density regions. We also present a study inspired by the road network and population density of Santiago, Chile, showing that our continuous approximation model can reliably guide CDP network sizing decisions in a realistic setting. This study provides managerial insights for understanding and designing cost-efficient urban parcel distribution systems.