A mixed integer linear programming model for optimal planning of bicycle sharing systems: A case study in Beijing

This paper investigates optimal planning of a bicycle sharing system (BSS) from an integrated and long-term perspective, namely by combining strategic design and operation decisions in an integrated way while considering the stochastic demand and service level. The methodological contribution of the current research effort is to propose a unified mixed integer linear programming (MILP) model, in which several sub-problems such as the number, location, and capacity of bicycle stations; total fleet size design; depot location design; and rebalancing and maintenance plans are combined and can be solved together. A scenario-based approach is applied to deal with stochastic demand. Also, the concept of subjective distance is proposed to characterize the coverage area of bicycle stations, which together with the availability rate for bicycles are set as metrics of the service level. A case in Beijing, China is studied and sensitivity analyses are performed for key parameters. To illustrate the practical value of the proposed approach, a comparison between the planning results solved by the proposed MILP model with the BSS in real life regarding station layout is also undertaken. From the results, we observe that a balance between the costs borne by the operator and the service level for users can be achieved. The stations are distributed evenly across the study area, which could increase the coverage and thus enhance the convenience of the service. The model developed can be employed by BSS operators for the planning decisions.