Time-dependent electric vehicle-drone routing problem for scheduled deliveries and on-demand pickups considering variable drone speeds and no-fly zones

This paper introduces the time-dependent electric vehicle-drone routing problem for scheduled deliveries and on-demand pickups considering variable drone speeds and no-fly zones (TDEVDRP-SDOP-VDS-NZ), involving multiple electric vehicles (EVs) and unmanned aerial vehicles (UAVs) to serve scheduled delivery customer requests (SDCRs) and on-demand pickup customer requests (OPCRs) with deadlines, while considering time-dependent EV speeds, variable drone speeds and no-fly zones. For TDEVDRP-SDOP-VDS-NZ, a route-based Markov decision process (MDP) model is formulated to maximize rewards, and the offline-online heuristic algorithm (OOHA) is proposed, combining the static EV-UAV joint delivery routes with online OPCR insertions. Experimental results show a 0.23 % decrease in average reward compared to the perfect-information counterpart, with deterministic scenarios achieving an average reward higher than uncertain scenarios. OOHA outperforms two benchmark algorithms, with gaps ranging from −6.57 % to −0.31 %. As the degree of dynamism increases, both rewards and OPCR acceptance ratios decrease. Rewards drop by over 10% when the degree of dynamism rises from 0.2 to 0.5, while higher variability leads to an increase in rewards. The average online processing time remains under 0.2 s, allowing the system to quickly respond to new OPCRs in real-time. OOHA demonstrates strong stability across different customer distributions. Sensitivity analysis reveals that an increase in the number of no-fly zones decreases both rewards and the ratio of OPCRs served by UAVs, particularly the ratio, which drops by over 16%. Sensitivity analysis of UAV flight speeds finds that variable drone speeds outperform maximum and minimum speeds, with maximum and minimum speeds leading to a more than 60% drop in the ratio of OPCRs served by UAVs. TDEVDRP-SDOP-VDS-NZ, although having a longer average online processing time compared to the model of Gu et al. (2023), is more in line with the actual distribution.