Mathematical models for the electric vehicle routing problem with time windows considering different aspects of the charging process

This paper addresses the electric vehicle routing problem with time windows (E-VRPTW), considering the battery’s state of charge ( $$SoC$$ SoC ) and the recharging process's linearity and non-linearity. We compare two proposed models: the first assumes a linear charging process, and the second evaluates the impact generated by including the non-linearity of the battery recharging process. The non-linear model considers the limitation of the state of charge and restricts the deep battery discharge during movement. Additionally, the effect of overload on the supplied energy process has been evaluated to extend the batteries' useful life. The models are tested on instances commonly used in the literature. The obtained results verify that including the non-linearity recharging process reduces the total time of the routes. Indeed, by accessing the upper sections of the recharge curve ( $$> 85\% \; SoC$$ > 85 % S o C , the more significant degradation), autonomy is obtained to avoid unnecessary visits to stations. In addition, including the option to carry out a fast recharge could reduce the total time, even reducing the number of vehicles necessary to carry out the delivery tasks and the maximum time defined by each route.