Static bike repositioning problem with heterogeneous distribution characteristics in bike sharing systems

Bike sharing is one of the recent trends in urban areas as a solution for the mobility problem, where it is seen as a significant component of local transportation due to the need to ensure last-mile transportation. Bike sharing systems enable bicycles to be rented at a station for a ride and be dropped off at another station which provides flexibility to users. However, incorporating a bike sharing system into the transportation network of a city involves its own challenges including balancing the supply and demand within stations, and scheduling bikes' repositioning. The bike repositioning scheduling problem arises due to the variable demand for various types of bicycles that can be rented from and left to any station. In order to ensure sustainability in bike sharing operations, bikes should be redistributed to the stations considering the demand, during for example a day or night. In this context, with the ultimate motivation of proposing a bike sharing system to meet within-day demand dynamics in a metropolitan city, we address the Static Bike sharing Rebalancing Problem (SBRP) with multiple capacitated vehicles for redistribution of bicycles. On purpose, we formulate a mixed-integer linear program in which the objective is minimizing the total cost subject to a set of constraints including truck capacity, demand satisfaction, inventory balance, and flow preservation. We have obtained the results from solutions to the SBRP through a real case study discussing the tendency on bike sharing systems before and during Covid-19 pandemic, in which total distance traveled according to the repositioning schemes for different months in a year, repositioning, and the truck type requirements for different days in a week, and the unsatisfied demand concerning the actual demands are analyzed. Computational experiments have shown that the distance traveled by trucks varies for the days of the week in different months of the year depending on the change in demand.