Cities, retailers, and delivery services are trying to find more environmental friendly solutions for last mile delivery. One very promising and partly used option are cargo bicycles. A critical factor of cargo bicycles is their travel speed, which depends on the mass of the load and the gradient of the chosen streets. Therefore, we define load-dependent travel speed and introduce the vehicle routing problem with load-dependent travel times (VRPLTT). We introduce a mixed-integer programming formulation and show the benefits of considering load-dependent travel times in last mile delivery with cargo bicycles. To efficiently solve larger instances, we develop an adaptive large neighborhood search (ALNS). For the numerical study, we introduce a new set of instances and show that the travel time can be reduced by 4.5% on average and up to 22% compared to the vehicle routing problem with time windows. Moreover, ignoring the load-dependent travel times can lead to the underestimation of travel time in such a way that time windows are violated.

城市、零售商和送货服务正在努力为最后一英里的送货寻找更环保的解决方案。一种非常有前途且部分使用的选择是货运自行车。货运自行车的一个关键因素是它们的行驶速度，这取决于负载的质量和所选街道的坡度。因此，我们定义了与负载相关的行驶速度，并引入了与负载相关的行驶时间（VRPLTT）的车辆路径问题。我们引入了混合整数规划公式，并展示了在货运自行车的最后一英里交付中考虑与负载相关的旅行时间的好处。为了有效地解决更大的实例，我们开发了自适应大邻域搜索 (ALNS)。对于数值研究，我们引入了一组新的实例，并表明旅行时间可以减少 4。与有时间窗的车辆路径问题相比，平均为 5%，最高可达 22%。此外，忽略与负载相关的行程时间会导致对行程时间的低估，从而违反时间窗。