Stochastic bi-objective optimisation formulation for bike-sharing system fleet deployment

Bike-sharing schemes (BSSs) have gained popularity as an alternative mode of transportation to solve the first/last mile problem. However, the bike-share market is subject to an oversupply problem with a low fleet utilisation rate in many countries. The aim of this paper is to tackle the BSS optimisation problem under stochastic demand scenarios by determining the shared bicycle fleet size and a fleet deployment strategy, where the interests of multiple stakeholders are taken into consideration at the same time. A stochastic multi-period bi-objective optimisation model is formulated to maximise the profit of bike-share operators and minimise the unmet demand, controlling the bike fleet utilisation rate. The problem is solved by an augmented ε-constraint method (Augmecon), which generates a set of non-dominated solutions. The numerical test is conducted with real data from Citi Bike to evaluate the validity of the model formulation and the effectiveness of the solution algorithm. The effect of fleet utilisation rate on BSS is analysed, where the trade-offs among earned profit, service level and fleet utilisation rate are addressed.