A static user-based bike inventory rebalancing problem considering equity

Abstract

Bicycles provide convenient and environmentally friendly transportation services. Because of its green and environmentally friendly mode, more and more cities operate Public Bike Sharing Systems all over the world to complement the public transit system. In Public Bike Sharing Systems, users can rent and return bikes at designed bike stations with bikes and docks. However, due to the user's asymmetric travel behavior, bike stations often become imbalanced. The deficient supply of bikes for rent and docks for returns in bike-sharing systems will affect bike users' satisfaction. One way to alleviate the imbalanced situation in bike-sharing systems is by user-based bike repositioning. Compared with traditional vehicle-based bike repositioning, user-based bike repositioning incentivizes travelers to help redistribute bikes, which not only helps operators save reposition costs but also makes contributions to the environment. Existing bike-sharing studies mainly focus on minimizing total imbalanced stations or demand dissatisfaction while ignoring the unequal demand dissatisfaction levels of stations. This unequalness can be considered inequity. This study aims to develop a new mathematical model considering elastic traveler demand and inequity in bike-sharing systems. It is formulated as a Mixed Integer Nonlinear and Nonconvex Programming model to minimize the weighted sum of the total incentive costs, the total imbalanced penalties of stations, and the penalties due to inequity among stations. The inequity is quantified by the sum of the absolute difference between imbalances among stations. The model assumes that travelers are sensitive to the incentives and incorporates the elastic nonlinear demand function. To deal with the nonlinear and nonconvex term, this study develops a new effective inner-approximation algorithm to obtain its -optimal solution. It can solve the problem accurately and sufficiently in small-scale bike networks. This study applies the modified artificial bee colony algorithm to solve large-size network problems.