The service points’ location and capacity problem

We study the design of a network of automatic parcel lockers to facilitate the last-mile delivery of small parcels where parcels are delivered via service points near their recipients’ home addresses. The recipients then pick up their parcels at convenient times. This method saves a substantial share of the handling and transportation costs associated with the parcel delivery process. The deployment of such a network requires decisions regarding the location and capacity of the service points. If a parcel has to be delivered through a service point with no remaining capacity, the parcel is sent directly to the recipient's address at a higher cost, or its delivery is postponed. Hence, there is a trade-off between the fixed setup cost, the variable operational cost, and the quality of the service. In this study, we take a bottom-up approach to the problem. We start by analyzing the dynamics of a single service point and show how to calculate a function that maps the parameters of its environment to the expected number of parcels that will be rejected from service or postponed. We then embed these functions in a mathematical model that optimizes the configuration of the network while considering the trade-offs described above.