Optimal rebalancing and charging of shared electric scooters using charging hubs

This paper addresses the overnight e-scooter rebalancing and charging problem in which e-scooters can be charged at a set of capacitated charging hubs. Operators use capacitated vehicles to collect e-scooters that need charging, drop them off at the hubs for charging, and pick them up later for repositioning. First, a discrete mathematical formulation is presented to optimize the drop-offs and pickups of e-scooters, as well as the routing/scheduling of vehicles. E-scooters of different states of charge (SoC) are modeled as multiple commodities linked through an SoC transition function. To reduce computational burdens, a discrete–continuous hybrid model is developed such that asymptotic vehicle routing formulas can be used to approximate local tour lengths and operational costs, and at the same time provide guidelines for building near-optimum feasible solutions. The hybrid model produces close approximations to the feasible solution in short times and shows to be a potential tool for strategic decision-making. Numerical tests showed interesting interdependencies and trade-offs among the numbers and capacities of both hubs and vehicles. Running dispersed charging hubs, even smaller ones, could result in a superior system service than running a few centralized hubs.