Collection and delivery points (CDPs) allow logistics operators to consolidate multiple customer request deliveries 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. We propose a continuous approximation model that jointly recommends the optimal size of the CDP network and the allocation of economic incentives to customers choosing CDPs, with the goal of minimizing total expected costs. Furthermore, we present two novel approaches to enforce a chance constraint into our approximate model, ensuring that the average demand per CDP exceeds its capacity with a small enough probability. In our experiments, we show that CDPs alone can reduce costs by 16.9%, while offering incentives to customers increases potential savings to 28.0%. We find that CDPs are most beneficial in high-density areas, leveraging economies of scale, whereas incentives are more effective in low-density regions. We also examine a case study in Santiago, Chile, showing that our continuous approximation model can reliably guide CDP network design decisions in a realistic network setting. This study provides valuable insights for understanding and designing cost-efficient urban parcel distribution systems.