The vehicle routing problem with load-dependent travel times for cargo bicycles

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.