A parcel locker network as a solution to the logistics last mile problem

We consider the problem of designing a parcel locker network as a solution to the Logistics Last Mile Problem: Choosing the optimal number, locations, and sizes of parcel locekers facilities. The objective is to maximize the total profit, consisting of the revenue from customers who use the service, minus the facilities' fixed and operational setup costs, the discounts in the delivery costs for customers who need to travel in order to collect their parcels, and the loss of potential customers who are not willing to travel for service. The problem is expressed as a 0-1 integer linear program. We show that it is equivalent to the well-known Uncapacitated Facility Location Problem. We then solve the modified problem, and apply it to an industrial-sized network.