Stochastic fleet deployment models for public bicycle rental systems

Abstract

This paper presents two stochastic bike deployment (SBD) models that determine the optimal number of bicycles allocated to each station in a leisure-oriented public bicycle rental system with stochastic demands. The SBD models represent the stochastic demands using a set of scenarios with given probabilities. A multilayer bike-flow time-space network is constructed for developing the models, where each layer corresponds to a given demand scenario and effectively describes bicycle flows in the spatial and temporal dimensions. As a result, the models are formulated as the integer multi-commodity network flow problem, which is characterized as NP-hard. We propose a heuristic to efficiently obtain good quality solutions for large-size model instances. Test instances are generated using real data from a bicycle rental system in Taiwan to evaluate the performance of the models and the solution algorithm. The test results show that the models can help the system operator of a public bicycle system make effective fleet deployment decisions.