Summary: To achieve logistic efficiency and customer convenience in last-mile delivery processes, a system with alternative delivery points in the form of locker box stations can be used. In such a system, customers can be served either at their home address within a certain time window, or at a locker box station where parcels can be picked up at any time. Customers can get a compensation payment when being served at a locker box. They can have a request of more than one parcel and the parcels can be of different sizes. At a locker box station, a limited number of slots of different sizes is available; we assume that parcels of one customer can be stored together in a slot. We consider the vehicle routing problem with heterogeneous locker boxes, where the total cost – consisting of routing and compensation costs – has to be minimized while taking into account the packing of parcels into locker boxes. We provide a mathematical formulation of the problem and propose a metaheuristic solution method. Instances and results from the literature for the problem with a single parcel and a single slot size are used to benchmark our metaheuristic solution method. For the problem with different sizes, we compare a unit-size model to a multi-size model, packing being considered in the latter. Finally, we analyze how different configurations of locker box stations work for different demand scenarios.