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 parking time in the objective and minimizes the completion time of the delivery tour. Parking time represents the process of the delivery person searching for a parking spot and then parking the vehicle at the chosen location. 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 parking time is large enough for the CDPP optimal solution to differ from this TSP solution. 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 parking time is high. This analysis provides immediate ways to improve routing in last-mile delivery.

停车是传统最后一英里配送实践的必要组成部分，但寻找停车位可能很困难。然而，路线文献很大程度上没有考虑寻找停车位的需要。在本文中，我们通过停车能力传递问题（CDPP）来解决寻找停车位的挑战。与文献中的其他模型不同，CDPP 考虑了目标中的停车时间，并最大限度地减少了送货行程的完成时间。停车时间代表送货员寻找停车位并将车辆停放在选定位置的过程。当我们将客户地理限制在完整的网格中时，我们确定了停放在每个客户处的旅行商问题 (TSP) 解决方案何时是 CDPP 的最佳解决方案的条件。然后，我们确定停车时间何时足够长，使得 CDPP 最优解与 TSP 解不同。我们为 CDPP 引入了一种启发式方法，可以快速找到大型实例的高质量解决方案。计算实验表明，停车对于最后一英里配送优化至关重要。 CDPP 优于行业实践和文献中的模型，在停车时间较长时显示出最大的优势。该分析提供了改进最后一英里配送路线的直接方法。