Operations with Electric Vehicles (EVs) on logistic companies and power utilities are increasingly related due to the charging stations representing the point of standard coupling between transportation and power networks. From this perspective, the Multi-depot Electric Vehicle Routing Problem (MDEVRP) is addressed in this research, considering a novel hybrid matheheuristic approach combining exact approaches and a Chu-Beasley Genetic Algorithm. An existing conflict is shown in three objectives handled through the experimentations: routing cost, cost of charging stations, and increased cost due to energy losses. EVs driving range is chosen as the parameter to perform the sensitivity analysis of the proposed MDEVRP. A 25-customer transportation network conforms to a newly designed test instance for methodology validation, spatially combined with a 33 nodes power distribution system.

Electric vehicle routing models are typically deterministic. However, stochastic vehicle routing models rarely include a battery constraint. This study addresses that gap with a two-stage stochastic mixed-integer programme for electric vehicle routing with time windows, in which routing, load, and load-dependent energy are first-stage decisions and travel-time-driven lateness is a second-stage recourse. Load and battery charge are proved scenario-invariant given any fixed route, collapsing the recourse to a timing sub-problem and yielding an exact multi-cut Benders decomposition with finite-convergence and complexity results. The formulation was implemented and solved with an open-source solver; this process identified and corrected three formulation defects, each documented. On Solomon-benchmark instances scaling from 3 to 20 customers, the implementation reproduces an independent hand calculation exactly, remains solver-certified optimal throughout, and shows empirical solve time scaling approximately with the square of the decision variable count (R²=0.99). This study also reports a value-of-the-stochastic-solution analysis, a battery-capacity threshold effect, and a robustness finding: time-window width, not spatial distribution, drives resilience to travel-time uncertainty. Scope limitations are stated explicitly, with full-scale benchmarking left as future work.