In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new "Markov chain dockless bike-sharing fleet size solution" algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.The bike-sharing deployed by merchants since 2016 are mainly dockless bicycles [10]. Compared with traditional docked bicycles, it could allow users to pick up and drop off bikes freely instead of at the designated station [11]. The dockless bike-sharing adopts the operation mode of "smart dockless", "GPS positioning", "network convenient payment" and "requesting on demand". It has become a popular way for short-distance green travel in China.The emergence of dockless bike-sharing is an innovative model of the sharing economy in the Internet era, which facilitates the daily short-distance travel of the public [12]. However, on the other hand, the disordered deployment of dockless bike-sharing has become an increasingly serious problem, because some bike-sharing companies try to keep the competition by blind expansions. The problems of fleet size and rebalancing [13][14][15] of the dockless bike-sharing stations are mainly illustrated as follows:•There are too many bicycles in some stations, but the problems of idleness are prominent, which even hinders the passage of pedestrians and cars. In contrast, the number of bicycles in some other stations is not enough to meet the needs of users.
•The response of the bike-sharing replenishment or repositioning transport is not so efficiently, and the rationality of the rebalancing is still a concern.Therefore, the fleet size and rebalancing of dockless bike-sharing stations are in urgent need of scientific analysis. It is necessary to propose an algorithm to determine the number of shared bicycles rationally and quickly at each station to achieve the goal of standardized management....