As an emerging mode of urban transportation, the shared electric micromobility system, with e-bike sharing and e-scooter sharing as the main typical representatives, is expanding rapidly because of its advantages of relieving traffic congestion and reducing emissions. The shared electric micromobility system provides users with rental services of electric micro-vehicles by setting up dockless stations defined by electric fences, which requires daytime dynamic battery swapping to ensure the normal operation of the system. The existing method divides the daytime operation horizon into several periods with the same length and solves a pure vehicle routing problem (VRP) at the beginning of each period, where the swapping demand of each station is equal to the number of low-power electric micro-vehicles in the station at that beginning moment. However, due to the absence of inventory management, this VRP-based strategy fails to consider the coordination between the inventory level and the riding demand of the station, resulting in untimely battery swapping or unnecessary station visit in some periods. To this end, we propose a battery swapping strategy with a predictive inventory routing method that plans the swappers’ routes, specific station visiting moments, and the number of swapped batteries of stations in each period, which spans the entire daytime planning horizon.

  First, because the shared electric micromobility system is highly dynamic over time under user behaviors, to predict the evolution of the station inventory level and the system performance, we propose a continuous time Markov model based on the historical transaction data for a single period, in which the inventory state of the station is defined by the number of shared electric micro-vehicles and their power level. With the initial inventory state, the prediction model gives the station's inventory level at different moments in the period. And since the inventory replenishment adopts the order-up-to level policy, i.e., the swapper swapping batteries for all the low-power electric micro-vehicles in the station when he arrives, it obtains the expected swapped batteries number of the station. Based on the predictions of inventory levels under the battery swapping behaviors and user behaviors, we define the metric of the expected successful riding (ESR) of the station in the period, which is used to calculate the expected revenue. After extending the prediction model across multiple periods to cover the entire planning horizon, we discretize the time for efficient calculation, where the arrival and departure rates of electric micro-vehicles at the station are constant in each discretized time slot.

  Then, utilizing the predictive information, we model the battery swapping problem as an inventory routing problem (IRP) to maximize the system's expected profit (expected revenue minus expected battery cost and truck travel cost) and give the corresponding mixed integer programming model, which considers the swapper’s waiting time in the station. Model constraints are composed of route constraints, time and capacity constraints for trucks, and system evolution constraints. The swapper can return to the battery warehouse midway to reload the fully charged battery, but the swapping mission must be completed before the end of the period. The station can be visited by a swapper once or not in each period.

  Finally, because the problem is NP-hard, we develop a decomposition-based adaptive large neighborhood search (ALNS) algorithm to solve it. The algorithm performs iterations between two interacting subproblems until the stop condition is triggered. It first decomposes the primal model into a distribution subproblem and a routing subproblem. The former replaces the truck travel cost with path-related transportation cost, using the commercial solver to give an optimal solution for whether and at which time slot the station is visited under the predictive information, which is passed to the routing subproblem. The latter performs the ALNS on the routes of swappers in each period, under the constraint that certain stations must be visited in the period, which embeds the components designed for the problem that contain the waiting time adjustment procedure and the optimal slot allocation dynamic programming for stations in the same route. The results of the routing subproblem update the factor of the path-related transportation cost in the distribution subproblem.

  We conducted long-term simulation experiments on a real shared e-micromobility system, the e-bike sharing system in Xiamen, China, for five working days. The results show that, compared with the existing VRP-based strategy, the IRP-based strategy can significantly improve the system's profit by around 33% on average through better cost control at the premise of sacrificing a certain service level. In addition, some important managerial insights can be summarized from the results of further sensitivity analysis. First, because the IRP-based strategy requires less battery swapping and truck travel, it can reduce investment costs of batteries and carbon emissions in the system’s operation. Second, the IRP-based strategy has a more stable profit performance under different daytime battery swapping frequencies, which can better cope with unexpected situations such as the unavailability of swappers or the need to deploy swappers across systems, improving the flexibility of operation management. Third, the commercial company can adopt different strategies in different market stages. In the initial stage of providing service, it is wise to utilize the advantages of the VRP-based strategy at the service level to cultivate user habits and seize the market. In the later stage, adopting the IRP-based strategy can improve the profit and reduce the pressure on the system’s operational management.