Collection and delivery points (CDPs) allow logistics operators to consolidate multiple customer delivery requests on a single vehicle stop, 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 the customer’s 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 decides on the network’s optimal number of CDPs and the economic incentive offered to customers who choose to be served at CDPs. The incentive is strategically relevant because it induces customers to pick up their orders farther from home, thereby affecting the optimal CDP network size. Furthermore, we equip our model with a chance constraint limiting the probability that the average demand per CDP exceeds its capacity. In our experiments, we show that CDPs alone cut expected costs by 16.9%, while offering incentives to customers increases potential savings to 28.0%. As an insight, we find that CDPs are most beneficial in high-density areas, in which they leverage economies of scale, whereas incentives are more effective in low-density areas. Additionally, our analysis suggests that providing CDPs to logistics operators at no cost has the potential to reduce their distribution costs by up to 60%, making it a potential government policy to lower emissions. We also examine a case study in Santiago, Chile, showing that our continuous approximation model can reliably guide CDP network sizing decisions in a realistic setting. This study provides valuable insights for understanding and designing cost-efficient urban parcel distribution systems.