In China, based on the mobile Internet technology and global positioning system (GPS), innovative bike-sharing is different from traditional bike-sharing system with docking station, for its flexibility and convenience. However, innovative bike-sharing system faces operational challenges, especially in faulty bike-sharing recycling (FBSR) problem. In this paper, a framework is designed based on the optimization method to solve the FBSR problem so that it can minimize the total recycling costs by taking the route optimization and loading capacity ratio as constraints. The FBSR method combines the K-means method for clustering faulty bikesharing with planning recycling route for operational decisions. Moreover, CPLEX solver is used to obtain the desired result of the FBSR model. Finally, a case study based on a certain area in Beijing, China, is used to verify the validity and applicability of the model. The results show that the value of loading capacity ratio and the number of clustering points greatly affect the results of FBSR problem. Four vehicles are designated to execute FBSR tasks required by different clustering points. This study is of considerable significance for the bike-sharing promotion in the last-mile situation to the real problems arising in the initial period.
A time-space network based optimization method is designed for high-speed rail train timetabling problem to improve the service level of the high-speed rail. The general time-space path cost is presented which considers both the train travel time and the high-speed rail operation requirements: (1) service frequency requirement; (2) stopping plan adjustment; and (3) priority of train types. Train timetabling problem based on time-space path aims to minimize the total general time-space path cost of all trains. An improved branch-and-price algorithm is applied to solve the large scale integer programming problem. When dealing with the algorithm, a rapid branching and node selection for branch-and-price tree and a heuristic train time-space path generation for column generation are adopted to speed up the algorithm computation time. The computational results of a set of experiments on China’s high-speed rail system are presented with the discussions about the model validation, the effectiveness of the general time-space path cost, and the improved branch-and-price algorithm.
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