Pick-Up Points (PUPs) represent an alternative delivery option for online purchases. Parcels are delivered at a reduced cost to PUPs and wait until being picked up by customers or returned to the original warehouse if their sojourn time is over. When the chosen PUP is overloaded, the parcel may be refused and delivered to the next available PUP on the carrier tour. This paper presents and compares forecasting approaches for the load of a PUP to help PUP management companies balance delivery flows and reduce PUP overload. The parcel life-cycle has been taken into account in the forecasting process via models of the flow of parcel orders, the parcel delivery delays, and the pick-up process. Model-driven and data-driven approaches are compared in terms of load-prediction accuracy. For the considered example, the best approach (which makes use of the relationship of the load with the delivery and pick-up processes) is able to predict the load up to 4 days ahead with mean absolute errors ranging from 3.16 parcels (1 day ahead) to 8.51 parcels (4 days ahead) for a PUP with an average load of 45 parcels.