In this paper, a bike repositioning problem with stochastic demand is studied. The problem is formulated as a two-stage stochastic programming model to optimize the routing and loading/unloading decisions of the repositioning truck at each station and depot under stochastic demands. The goal of the model is to minimize the expected total sum of the transportation costs, the expected penalty costs at all stations, and the holding cost of the depot. A simulated annealing algorithm is developed to solve the model. Numerical experiments are conducted on a set of instances from 20 to 90 stations to demonstrate the effectiveness of the solution algorithm and the accuracy of the proposed two-stage stochastic model.

中文翻译：

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解决自行车共享系统中的自行车重新定位问题：一个两阶段随机规划模型

在本文中，研究了具有随机需求的自行车重新定位问题。该问题被表述为两阶段随机规划模型，以在随机需求下优化重新定位卡车在每个站点和仓库的路线选择和装载/卸载决策。该模型的目标是使运输成本、所有站点的预期惩罚成本和仓库持有成本的预期总和最小。开发了一种模拟退火算法来求解该模型。在 20 到 90 个站点的一组实例上进行了数值实验，以证明求解算法的有效性和所提出的两阶段随机模型的准确性。