Managing shared electric micromobility systems: Allocation planning and battery swapping

Using electric micromobility vehicles, shared electric micromobility systems provide an environmental mode of short-distance travel within a city. Given the inescapable costs of vehicles and batteries, and the necessity for the system operator to manage the state-of-charge of vehicles through battery swapping to effectively meet uncertain demands, it is pivotal to accurately determine the initial allocation of vehicles and batteries, as well as to manage battery swapping during operations under uncertainties. Therefore, we formulate a two-stage stochastic program. In the first stage, the operator decides allocation of vehicles and spare batteries. In the second stage, it determines vehicle operations and battery swapping in various regions over a time horizon. To enhance computational efficiency, we develop alternating direction method of multipliers (ADMM) to decompose the stochastic problem into several deterministic subproblems and iteratively solve them in parallel. We show the obtained solutions converge when iteration step m approaches infinity, with their accumulation point satisfying the KKT conditions. Moreover, we show ADMM converges at a rate of O(1/m). Our numerical results suggest that ADMM outperforms a commercial solver in computational time, reducing it by up to 96.5%. We reveal that raising allocation capacity increases the allocation of vehicles and batteries, but the allocation growth rate diminishes as capacity rises further. The operator prefers to swap batteries once they are depleted rather than preparing full-energy ones in advance. A higher charging speed lowers battery allocation but has a limited impact on vehicle allocation and service level.