A Stochastic Maximal Covering Formulation for a Bike Sharing System

This paper discusses a maximal covering approach for bike sharing systems under deterministic and stochastic demand. Bike sharing is constantly becoming a more popular and sustainable alternative transportation system. One of the most important elements for the design of a successful bike sharing system is given by the location of stations and bikes. The demands in each zone for each period is however uncertain and can only be estimated. Therefore, it is necessary to address this problem by taking into account the stochastic features of the problem. The proposed model determines the optimal location of bike stations, and the number of bikes located initially in each station, considering an initial investment lower than a given predetermined budget. The objective of the model is to maximize the percentage of covered demand. Moreover, during the time horizon, it is possible to relocate a certain amount of bikes in different stations with a cost proportional to the traveled distance. Both deterministic and stochastic models are formulated as mixed integer linear programs.