  Parking is a necessary component of traditional last-mile delivery practices,
but finding parking can be difficult. Yet, the routing literature largely does
not account for the need to find parking. In this paper, we address this
challenge of finding parking through the Capacitated Delivery Problem with
Parking (CDPP). Unlike other models in the literature, the CDPP accounts for
the search time for parking in the objective and minimizes the completion time
of the delivery tour. When we restrict the customer geography to a complete
grid, we identify conditions for when a Traveling Salesman Problem (TSP)
solution that parks at each customer is an optimal solution to the CDPP. We
then determine when the search time for parking is large enough for the CDPP
optimal solution to differ from this TSP solution. We also identify model
improvements that allow reasonably-sized instances of the CDPP to be solved
exactly. We introduce a heuristic for the CDPP that quickly finds high quality
solutions to large instances. Computational experiments show that parking
matters in last-mile delivery optimization. The CDPP outperforms industry
practice and models in the literature showing the greatest advantage when the
search time for parking is high. This analysis provides immediate ways to
improve routing in last-mile delivery.
