Abstract: After a frenzied expansion, the operation management in shared bicycle industry needs urgent improvements due to out bursting problems. This article aims at solving the over-deployment problem by constructing an optimization model to optimize the amount of bicycles supplies. Firstly, based on analyzing and describing how the shared bicycle system operates, the core research issues involved in bicycle deployment optimization is clarified. The research scope focuses on the deployment session. Under the framework of space-time subdivision, Markov chain and state transition matrix are used to analyze and describe the time-varying process of bicycle distribution between stations. Descripting the service level of the shared bicycle system in terms of demand-met probability, the bicycle demand at each deployment station is computed according to certain service level constraints. Based on these analysis and description, three core issues involving bicycle deployment optimization are put forward. These issues includes what is the optimal bicycle deployment under daily schedule scheme; what is the optimal deployment under once for all deployment without scheduling and how to handle the relationship between deployment amounts and re-scheduling frequency? Secondly, according to different bicycle re-scheduling schemes, combining with the constraints of the bicycle demand and the regularity of bicycle distribution along with time and space, the optimization models of bicycle deployment are constructed under different scheduling schemes. Based on analyzing the relation between the space of feasible solution and the optimal value of objective function, the natures of the optimal bicycle deployment is illustrated under different scheduling schemes. The results show that:(1) the subdivision of time and space is beneficial in better capturing demands and results in the increasing of optimal amount of bicycle deployment. (2) It is possible to reduce the amount of bicycle deployment by increasing the frequency of re-scheduling. However, the amount of bicycle deployment is limited with upper limit h_sum2^* and lower limit h_sum3^*. Finally, the data from a contest subject in 2017 College Mathematical Modeling Contest are used as a case study. By computing state transfer matrix and the demand of each deployment station, solving the optimization model numerically, how the model in this paper is applied is illustrated and verify the operability and effectiveness of the model in solving specific problems are verified. The model and corresponding solution process in this paper shed lights on solving optimization problem for resources allocation system.

Key words: bicycle sharing, service level, supply, Markov process