The mixed fleet vehicle routing problem with partial recharging by multiple chargers: Mathematical model and adaptive large neighborhood search

•Mixed Fleet Vehicle Routing Problem with Multiple Chargers (MF-VRP-MC) is addressed.•The MF-VRP-MC includes electric and internal combustion vehicles.•A mixed integer mathematical programming formulation for the MF-VRP-MC is developed.•An ALNS algorithm with new initialization and neighborhood mechanisms is proposed.•Computational results reveal that ALNS performs quite well on test instances. We introduce the Mixed Fleet Vehicle Routing Problem with Time Windows and Partial Recharging by Multiple Chargers (MF-VRP-MC). It composes of electric and internal combustion vehicles, and consolidates several aspects in a comprehensive unique model. The MF-VRP-MC considers travelled distance and carried load on vehicles in both emission and energy consumption functions. It deals with the minimization of total cost while satisfying customer delivery demands. First, we develop a mixed integer mathematical programming formulation for the MF-VRP-MC. Because of the NP-hardness of the problem, to solve medium and large-size instances, then we develop an Adaptive Large Neighborhood Search (ALNS) based algorithm with introducing new advanced neighborhood mechanisms to successfully handle complex problem constraints. Meantime, new approaches are tailored for boosting diversification effect in addition to new neighborhood scoring policy and new enhancement procedure. Furthermore, selection of recharging technology among the others at charging station is firstly considered in the solution phase of a mixed fleet problem. Extensive computational results indicate that our ALNS performs quite well on benchmark instances.