Continuous-Time Modeling for the Electric Vehicle Routing Problem with Flexible Charging Decisions Under Charging Station and Battery Capacity Constraints

In electric vehicle logistics, limited range and charging station capacity pose critical challenges to route planning, with direct implications for the sustainability of transportation systems. Conventional electric vehicle routing problem (EVRP) models that account for charger capacity typically rely on discrete-time approximations or fixed charging rules, failing to capture continuous-time waiting behavior or flexible charging decisions. These limitations may lead to additional vehicle dispatch, resulting in energy waste and increased carbon emissions. This study develops a novel EVRP model that simultaneously incorporates constraints on both station and battery capacity, and proposes a tailored genetic-algorithm-based heuristic to address computational challenges. The model innovatively employs a set of linear constraints to precisely represent limited chargers in continuous time, clearly distinguishing vehicle charging from waiting. Moreover, it enables vehicles to autonomously determine optimal charging amounts based on route and battery state, rather than following preset rules. Numerical results on an eight-customer instance show that the proposed model reduces total task completion time from 98.9 units to 60.4 units, a 38.9% improvement, compared to the conventional vehicle-count-based capacity constraint. On a 20-customer instance, the proposed heuristic obtains an objective value of 101.99 within 15 s, whereas Gurobi requires 205 s to achieve a marginally better value of 99.00. For a 60-customer network, the proposed GA converges within 30 s, and sensitivity analysis on charger availability further validates the model’s effectiveness. These results validate the model’s capability under limited charging resources and the algorithm’s scalability for time-sensitive logistics scheduling.