Integrated electric logistics vehicle recharging station location–routing problem with mixed backhauls and recharging strategies

The widespread application of electric vehicles for city last-mile logistics has been enhanced by the emerging trend of urban sustainable mobility, which intends to reduce vehicle emissions and the dependence on fossil fuels. The recharging facility location is critical for electric logistics network planning, because it significantly affects future operation costs and efficiency. This study proposes an integrated electric logistics vehicle recharging station location–routing problem with mixed backhauls and recharging strategies, which is formulated as a time-discretized multicommodity network flow optimization model based on a space–time–state–energy representation network. This study aims to optimize the selection of the recharging station location considering route planning with complicated constraints of recharging capacity, facility construction budget, vehicle loading capacity, battery remaining capacity, spatial structure of real road networks, mixed pickup and delivery requests, and service time windows. A hybrid Lagrangian relaxation and alternating direction method of multipliers (LR-ADMM) decomposition solution framework is constructed to decouple the proposed integrated problem into a recharging station location problem for strategic planning and an electric vehicle routing problem with mixed backhauls, time windows, and recharging strategies for operational decisions. These two subproblems are solved alternately by time-dependent forward dynamic programming algorithms embedded into the LR-ADMM framework. The solution quality is guaranteed by calculating the optimality gap between the best lower and upper bounds for each iteration. The experimental results based on the Sioux-Falls network and real-world West Jordan network prove the computational effectiveness and optimization quality of the proposed solution approach.