The location routing problem with time windows and load-dependent travel times for cargo bikes

Abstract

Last-mile delivery with traditional delivery trucks is ecologically unfriendly and leads to high road utilization. Thus, cities seek for different delivery options to solve these problems. One promising option is the use of cargo bikes in last-mile delivery. These bikes are typically released at micro hubs, which are small containers or facilities located at advantageous places in the city center. Since the bike’s travel speed depends on its remaining load and the street gradient, placing the hubs at valleys might cause additional work for rides. Therefore, the following question arises: How high is the impact of load-dependent travel times on micro hubs’ cost-optimal placements?

To answer this question, we introduce the location routing problem with time windows and load-dependent travel times. We formulate the problem as a mixed-integer linear program and introduce an adaptive large neighborhood search with a problem-specific procedure for micro hub placements and problem-specific operators to solve larger instances. In a numerical study, we find that load-dependent travel times significantly influence the location of hubs, following that hubs with a higher elevation are preferably used. Moreover, customers are served from hubs with a similar elevation. This would not be the case if load-dependent travel times are ignored, resulting in an increase in costs by up to 2.7$\text{\%}$ or, instead, to up to 26$\text{\%}$ infeasible solutions as time windows are not adhered to.